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Journal articles on the topic 'Maximal Solution'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Guo, Hongxia, Zongming Guo, and Fangshu Wan. "Radial symmetry of non-maximal entire solutions of a bi-harmonic equation with exponential nonlinearity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 6 (2019): 1603–25. http://dx.doi.org/10.1017/prm.2018.49.

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AbstractWe study radial symmetry of entire solutions of the equation0.1$$\Delta ^2u = 8(N-2)(N-4)e^u\quad {\rm in}\;R^N\;\;(N \ges 5).$$It is known that (0.1) admits infinitely many radially symmetric entire solutions. These solutions may have either a (negative) logarithmic behaviour or a (negative) quadratic behaviour at infinity. Up to translations, we know that there is only one radial entire solution with the former behaviour, which is called ‘maximal radial entire solution’, and infinitely many radial entire solutions with the latter behaviour, which are called ‘non-maximal radial entire

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2

Bubák, Milan, and Mirko Navara. "Fitting Copulas with Maximal Entropy." Entropy 27, no. 1 (2025): 87. https://doi.org/10.3390/e27010087.

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We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-f

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3

Mariotti, Marco. "Maximal symmetry and the Nash solution." Social Choice and Welfare 17, no. 1 (2000): 45–53. http://dx.doi.org/10.1007/pl00007174.

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4

Zagatti, Sandro. "Maximal generalized solution of eikonal equation." Journal of Differential Equations 257, no. 1 (2014): 231–63. http://dx.doi.org/10.1016/j.jde.2014.04.001.

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5

Bezukhov, D. A. "ESTIMATES OF POSITIVE NONTRIVIAL SOLUTIONS OF A DIFFERENTIAL EQUATION WITH POWER NONLINEARITY." Vestnik of Samara University. Natural Science Series 21, no. 6 (2017): 23–26. http://dx.doi.org/10.18287/2541-7525-2015-21-6-23-26.

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Differential equations in paper with power nonlinearity are considered. Solutions which are defined in some neighborhood of plus infinity are called proper solutions. It is proved that propersolution to the equation is kneser solution, which means that solution and it’s quasiderivatives change their signs and tend to zero. The integral representation for proper solutions is proved. Upper estimates for solution and it’s quasiderivatives for proper solutions with maximal interval of existence is positive semiaxis to the equation with quasiderivative are proved. Upper and lowerestimates of soluti

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6

Bulyno, D. A., A. L. Gladkov, and A. I. Nikitin. "Initial Boundary Value Problem for a System of Semilinear Parabolic Equations with Absorption and Nonlinear Nonlocal Boundary Conditions." Владикавказский математический журнал 27, no. 2 (2025): 5–18. https://doi.org/10.46698/o2548-3794-2309-a.

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In this paper we consider classical solutions of an initial boundary value problem for a~system of semilinear parabolic equations with absorption and nonlinear nonlocal boundary conditions. Nonlinearities in equations and boundary conditions may not satisfy the Lipschitz condition. To prove the existence of a solution we regularize the original problem. Using the Schauder--Tikhonov fixed point theorem, the existence of a local solution of regularized problem is proved. It is shown that the limit of solutions of the regularized problem is a maximal solution of the original problem. Using the pr

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7

Ouyang, Q. "DNA Solution of the Maximal Clique Problem." Science 278, no. 5337 (1997): 446–49. http://dx.doi.org/10.1126/science.278.5337.446.

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8

Pope, C. N., and N. P. Warner. "A Dielectric Flow Solution with Maximal Supersymmetry." Journal of High Energy Physics 2004, no. 04 (2004): 011. http://dx.doi.org/10.1088/1126-6708/2004/04/011.

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9

Hendren, William G., Dennis D. O'Keefe, Gillian A. Geffin, Alvin G. Denenberg, Tim R. Love, and Willard M. Daggett. "Maximal Oxygenation of Dilute Blood Cardioplegic Solution." Annals of Thoracic Surgery 44, no. 1 (1987): 48–52. http://dx.doi.org/10.1016/s0003-4975(10)62355-7.

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Hendren, William G., Dennis D. O'Keefe, Gillian A. Geffin, Alvin G. Denenberg, Tim R. Love, and Willard M. Daggett. "Maximal oxygenation of dilute blood Cardioplegic solution." Annals of Thoracic Surgery 58, no. 5 (1994): 1558–59. http://dx.doi.org/10.1016/0003-4975(94)91965-8.

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11

ZELENYUK, YEVHEN. "LEFT MAXIMAL AND STRONGLY RIGHT MAXIMAL IDEMPOTENTS IN G*." Journal of Symbolic Logic 82, no. 1 (2017): 26–34. http://dx.doi.org/10.1017/jsl.2016.62.

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AbstractLet G be a countably infinite discrete group, let βG be the Stone–Čech compactification of G, and let ${G^{\rm{*}}} = \beta G \setminus G$. An idempotent $p \in {G^{\rm{*}}}$ is left (right) maximal if for every idempotent $q \in {G^{\rm{*}}}$, pq = p (qp = P) implies qp = q (qp = q). An idempotent $p \in {G^{\rm{*}}}$ is strongly right maximal if the equation xp = p has the unique solution x = p in G*. We show that there is an idempotent $p \in {G^{\rm{*}}}$ which is both left maximal and strongly right maximal.

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12

Konaté, Ibrahime, Brahima Roamba, and Arouna Ouédraogo. "Convection-diffusion problems involving measure data and p(.)-anisotropic operator in variable exponent space." Gulf Journal of Mathematics 19, no. 1 (2025): 312–36. https://doi.org/10.56947/gjom.v19i1.2602.

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In this paper, we investigate a nonlinear diffusion-convection problem with measure data, involving a general anisotropic operator with variable exponent and a maximal monotone graph. Utilizing Yosida’s regularization, we apply an approximation technique to formulate a regularized problem. We then employ the theory of maximal monotone operators in Banach spaces to demonstrate the existence of at least one solution for the approximate problem. Subsequently, we show that the sequence of solutions to the approximate problem converges, in the limit, to a renormalized and/or entropic solution of th

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13

da Silva, João Vitor, Julio D. Rossi, and Ariel M. Salort. "Maximal solutions for the ∞-eigenvalue problem." Advances in Calculus of Variations 12, no. 2 (2019): 181–91. http://dx.doi.org/10.1515/acv-2017-0024.

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AbstractIn this article we prove that the first eigenvalue of the {\infty}-Laplacian\left\{\begin{aligned} \displaystyle\min\{-\Delta_{\infty}v,|\nabla v|-\lambda% _{1,\infty}(\Omega)v\}&\displaystyle=0&&\displaystyle\text{in }\Omega,\\ \displaystyle v&\displaystyle=0&&\displaystyle\text{on }\partial\Omega,\end{% aligned}\right.has a unique (up to scalar multiplication) maximal solution. This maximal solution can be obtained as the limit as {\ell\nearrow 1} of concave problems of the form\left\{\begin{aligned} \displaystyle\min\{-\Delta_{\infty}v_{\ell},|\nabla v_{% \el

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14

Oruganti, Shobha, Junping Shi, and Ratnasingham Shivaji. "Logistic equation with thep-Laplacian and constant yield harvesting." Abstract and Applied Analysis 2004, no. 9 (2004): 723–27. http://dx.doi.org/10.1155/s1085337504311097.

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We consider the positive solutions of a quasilinear elliptic equation withp-Laplacian, logistic-type growth rate function, and a constant yield harvesting. We use sub-super-solution methods to prove the existence of a maximal positive solution when the harvesting rate is under a certain positive constant.

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15

Yue, Yuan, and Yong-Qiang Wang. "Excited States of Maximal Warm Holes." Universe 9, no. 7 (2023): 338. http://dx.doi.org/10.3390/universe9070338.

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Recently, the Einstein–Maxwell–scalar model with a non-minimal coupling between the scalar and Maxwell fields was explored. As a result, a new class of black hole solutions with scalar hair was discovered. By fixing the mass of a black hole and taking the maximum allowable charge, an extremal black hole was obtained. Interestingly, this extremal black hole not only possesses an event horizon with a non-zero surface area but also exhibits a non-zero Hawking temperature. This unique type of extremal black hole is referred to as a maximal warm hole (MWH). In this paper, we revisit this model and

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16

Krzan, Marcel, Pradipta Chattopadhyay, Sandra Orvalho, and Maria Zednikova. "Effects of N-Alkanol Adsorption on Bubble Acceleration and Local Velocities in Solutions of the Homologous Series from Ethanol to N-Decanol." Materials 16, no. 5 (2023): 2125. http://dx.doi.org/10.3390/ma16052125.

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The influence of n-alkanol (C2–C10) water solutions on bubble motion was studied in a wide range of concentrations. Initial bubble acceleration, as well as local, maximal and terminal velocities during motion were studied as a function of motion time. Generally, two types of velocity profiles were observed. For low surface-active alkanols (C2–C4), bubble acceleration and terminal velocities diminished with the increase in solution concentration and adsorption coverage. No maximum velocities were distinguished. The situation is much more complicated for higher surface-active alkanols (C5–C10).

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17

A. M. A. El-Sayed, F. Gaafar, and M. El-Gendy. "On the maximal and minimal solutions of a nonlocal problem of a delay stochastic differential equation." Malaya Journal of Matematik 4, no. 03 (2016): 497–504. http://dx.doi.org/10.26637/mjm403/020.

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In this paper we are concerned with a problem of of a delay stochastic differential equation with nonlocal condition, the solution is represented as stochastic integral equation that contain mean square Riemann integral. We study the existence of at least mean square continuous solution for this problem. The existence of the maximal and minimal solutions will be proved.

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18

GU, LI, and GREGORY A. LAWRENCE. "Analytical solution for maximal frictional two-layer exchange flow." Journal of Fluid Mechanics 543, no. -1 (2005): 1. http://dx.doi.org/10.1017/s0022112005006002.

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19

Plagne, Alain, and Anne de Roton. "Maximal sets with no solution to x+y=3z." Combinatorica 36, no. 2 (2015): 229–48. http://dx.doi.org/10.1007/s00493-015-3100-4.

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20

Choquet-Bruhat, Y. "Solution of the Einstein constraints on non-maximal submanifolds." Classical and Quantum Gravity 10, S (1993): S205—S206. http://dx.doi.org/10.1088/0264-9381/10/s/024.

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21

Zhang, Lei-Hong, Li-Zhi Liao, and Li-Ming Sun. "Towards the global solution of the maximal correlation problem." Journal of Global Optimization 49, no. 1 (2010): 91–107. http://dx.doi.org/10.1007/s10898-010-9536-6.

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22

Whalley, D. W., P. D. Hemsworth, and H. H. Rasmussen. "Regulation of intracellular pH in cardiac muscle during cell shrinkage and swelling in anisosmolar solutions." American Journal of Physiology-Heart and Circulatory Physiology 266, no. 2 (1994): H658—H669. http://dx.doi.org/10.1152/ajpheart.1994.266.2.h658.

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The effect on intracellular pH (pHi) of exposure to solutions of progressively increasing osmolarity from 418 to 620 mosM and to hyposmolar solutions (240 mosM) was examined in guinea pig ventricular muscle using ion-selective microelectrodes. Exposure of tissue to 418 mosM Tyrode solution (100 mM sucrose added) produced an intracellular alkalosis of approximately 0.1 U, whereas exposure to 620 mosM solution (300 mM sucrose added) caused an intracellular acidosis of approximately 0.1 U. The maximal rate of recovery of pHi from acidosis induced by an NH4Cl prepulse increased progressively as ex

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23

Zhang, Yalong, Wei Yu, Xuan Ma, Hisakazu Ogura, and Dongfen Ye. "Multi-Objective Optimization for High-Dimensional Maximal Frequent Itemset Mining." Applied Sciences 11, no. 19 (2021): 8971. http://dx.doi.org/10.3390/app11198971.

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The solution space of a frequent itemset generally presents exponential explosive growth because of the high-dimensional attributes of big data. However, the premise of the big data association rule analysis is to mine the frequent itemset in high-dimensional transaction sets. Traditional and classical algorithms such as the Apriori and FP-Growth algorithms, as well as their derivative algorithms, are unacceptable in practical big data analysis in an explosive solution space because of their huge consumption of storage space and running time. A multi-objective optimization algorithm was propos

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24

Amick, C. J. "A problem in neural networks." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 118, no. 3-4 (1991): 225–36. http://dx.doi.org/10.1017/s0308210500029061.

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SynopsisIn this paper we consider a simple model for coupled nonlinear oscillators in a continuous medium. There is shown to exist a maximal branch of phaselocked solutions connecting the trivial one to a limiting singular solution.

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25

Whalley, D. W., L. C. Hool, R. E. Ten Eick, and H. H. Rasmussen. "Effect of osmotic swelling and shrinkage on Na(+)-K+ pump activity in mammalian cardiac myocytes." American Journal of Physiology-Cell Physiology 265, no. 5 (1993): C1201—C1210. http://dx.doi.org/10.1152/ajpcell.1993.265.5.c1201.

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The effect on the sarcolemmal Na(+)-K+ pump of exposure to anisosmolar solutions was examined using whole cell patch clamping and ion-selective microelectrodes. Na(+)-K+ pump currents were measured in single ventricular myocytes by using pipette Na+ concentrations ([Na]pip) of 0-70 mM. The relationship between [Na]pip and pump current was well described by the Hill equation. The [Na]pip for half-maximal pump current (K0.5) was 21.4 mM in isosmolar (310 mosM) solution. K0.5 was 12.8 mM during cell swelling in hyposmolar solution (240 mosM) and 39.0 mM during cell shrinkage in hyperosmolar solut

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26

El-Sayed, Ahmed M. A., Wagdy G. El-Sayed, and Somyya S. Amrajaa. "On a Boundary Value Problem of Hybrid Functional Differential Inclusion with Nonlocal Integral Condition." Mathematics 9, no. 21 (2021): 2667. http://dx.doi.org/10.3390/math9212667.

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In this work, we present a boundary value problem of hybrid functional differential inclusion with nonlocal condition. The boundary conditions of integral and infinite points will be deduced. The existence of solutions and its maximal and minimal will be proved. A sufficient condition for uniqueness of the solution is given. The continuous dependence of the unique solution will be studied.

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27

Salim, Mesbahi, and Imane Saffidine Khaoula. "Mathematical Analysis of a Degenerate Reaction-Diffusion Model." International Journal of Mathematics And Computer Research 10, no. 01 (2022): 2546–50. https://doi.org/10.47191/ijmcr/v10i1.04.

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In this paper, we are interested in the study of a degenerate reaction-diffusion model, where we prove the existence of positive maximal and minimal solutions, including the uniqueness of the positive solution. The technique used is mainly based on the method of upper and lower solutions.

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28

Bruehl, C., W. J. Wadman, and O. W. Witte. "Concentration Dependence of Bicarbonate-Induced Calcium Current Modulation." Journal of Neurophysiology 84, no. 5 (2000): 2277–83. http://dx.doi.org/10.1152/jn.2000.84.5.2277.

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High-voltage–activated calcium currents (HVA) of CA1 neurons are prominently attenuated following a switch from HEPES-buffered solution to one buffered with CO2/HCO3 −. In the present study we investigated whether bicarbonate ions or the dissolved CO2 induce this alteration in current characteristic. The study was carried out on freshly isolated CA1 neurons using the whole cell patch-clamp technique. Maximal calcium conductance and the mean peak amplitude of the currents showed a concentration-dependent decrease when cells were consecutively bathed in solutions containing increasing amounts of

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29

DÁVILA, JUAN. "GLOBAL REGULARITY FOR A SINGULAR EQUATION AND LOCAL H1 MINIMIZERS OF A NONDIFFERENTIABLE FUNCTIONAL." Communications in Contemporary Mathematics 06, no. 01 (2004): 165–93. http://dx.doi.org/10.1142/s0219199704001240.

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We prove optimal Hölder estimates up to the boundary for the maximal solution of a singular elliptic equation. The techniques used in this argument are applied to show that in some situations the maximal solution is a local minimizer of the corresponding functional in the topology of H1.

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30

Chong, Edwin, Kym J. Guelfi, and Paul A. Fournier. "Combined Glucose Ingestion and Mouth Rinsing Improves Sprint Cycling Performance." International Journal of Sport Nutrition and Exercise Metabolism 24, no. 6 (2014): 605–12. http://dx.doi.org/10.1123/ijsnem.2013-0097.

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This study investigated whether combined ingestion and mouth rinsing with a carbohydrate solution could improve maximal sprint cycling performance. Twelve competitive male cyclists ingested 100 ml of one of the following solutions 20 min before exercise in a randomized double-blinded counterbalanced order (a) 10% glucose solution, (b) 0.05% aspartame solution, (c) 9.0% maltodextrin solution, or (d) water as a control. Fifteen min after ingestion, repeated mouth rinsing was carried out with 11 × 15 ml bolus doses of the same solution at 30-s intervals. Each participant then performed a 45-s max

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31

Jia, Zhigang, Meixiang Zhao, Minghui Wang, and Sitao Ling. "Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/681605.

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The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.

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32

Markfelder, Simon. "A new convex integration approach for the compressible Euler equations and failure of the local maximal dissipation criterion." Nonlinearity 37, no. 11 (2024): 115022. http://dx.doi.org/10.1088/1361-6544/ad81c8.

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Abstract In this paper we establish a new convex integration approach for the barotropic compressible Euler equations in two space dimensions. In contrast to existing literature, our new method generates not only the momentum for given density, but also the energy and the energy flux. This allows for a simple way to construct admissible solutions, i.e. solutions which satisfy the energy inequality. Moreover using the convex integration method developed in this paper, we show that the local maximal dissipation criterion fails in the following sense: There exist wild solutions which beat the sel

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33

Yu, Song-Yue, and Baoqiang Yan. "Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion." Mathematics 9, no. 17 (2021): 2173. http://dx.doi.org/10.3390/math9172173.

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In this paper, the thermal explosion model described by a nonlinear boundary value problem is studied. Firstly, we prove the comparison principle under nonlinear boundary conditions. Secondly, using the sub-super solution theorem, we prove the existence of a positive solution for the case K(x)>0, as well as the monotonicity of the maximal solution on parameter λ. Thirdly, the uniqueness of the solution for K(x)<0 is proved, as well as the monotonicity of the solutions on parameter λ. Finally, we obtain some new results for the existence of solutions, and the dependence on the λ for the c

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34

KAWASHIMA, SHUICHI, and SHINYA NISHIBATA. "CAUCHY PROBLEM FOR A MODEL SYSTEM OF THE RADIATING GAS: WEAK SOLUTIONS WITH A JUMP AND CLASSICAL SOLUTIONS." Mathematical Models and Methods in Applied Sciences 09, no. 01 (1999): 69–91. http://dx.doi.org/10.1142/s0218202599000063.

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This paper deals with the global existence and the time asymptotic state of solutions to the initial value problems for the system derived from approximating a one-dimensional model of a radiating gas. When the spatial derivative of the initial data is larger than a certain negative critical value, a unique solution exists globally in time. But if it is smaller than another negative critical value, the spatial derivative of the corresponding solution blows up in a finite time. Thus it is natural to think about weak solutions in a suitable sense. As a prototype of weak solutions, we consider th

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35

Shi, Piao-Piao, and Wen-Xia Wang. "Infinite Boundary Value Problems for Second-Order Nonlinear Impulsive Differential Equations with Supremum." Discrete Dynamics in Nature and Society 2010 (2010): 1–15. http://dx.doi.org/10.1155/2010/393757.

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We investigate the infinite boundary value problems for second-order impulsive differential equations with supremum by establishing a new comparison result and using the lower and upper solution method, and obtain the existence results for their maximal and minimal solutions.

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36

Ibrahim, Rabha W., and Hamid A. Jalab. "Time-Space Fractional Heat Equation in the Unit Disk." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/364042.

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We will study a maximal solution of the time-space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann-Liouville operator, while the fractional space is assumed in the Srivastava-Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions.

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Gu, Yu, Takeshi Tsukada, and Hiroshi Unno. "Optimal CHC Solving via Termination Proofs." Proceedings of the ACM on Programming Languages 7, POPL (2023): 604–31. http://dx.doi.org/10.1145/3571214.

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Motivated by applications to open program reasoning such as maximal specification inference, this paper studies optimal CHC solving , a problem to compute maximal and/or minimal solutions of constrained Horn clauses (CHCs). This problem and its subproblems have been studied in the literature, and a major approach is to iteratively improve a solution of CHCs until it becomes optimal. So a key ingredient of optimization methods is the optimality checking of a given solution. We propose a novel optimality checking method, as well as an optimization method using the proposed optimality checker, ba

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Liu, Xiping, Fanfan Li, Mei Jia, and Ertao Zhi. "Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/758390.

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We study the existence and uniqueness of the solutions for the boundary value problem of fractional differential equations with nonlinear boundary conditions. By using the upper and lower solutions method in reverse order and monotone iterative techniques, we obtain the sufficient conditions of both the existence of the maximal and minimal solutions between an upper solution and a lower solution and the uniqueness of the solutions for the boundary value problem and present the iterative sequence for calculating the approximate analytical solutions of the boundary value problem and the error es

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Chen, Peng, Xinguang Zhang, Lishuang Li, Yongsheng Jiang, and Yonghong Wu. "Existence and Asymptotic Estimates of the Maximal and Minimal Solutions for a Coupled Tempered Fractional Differential System with Different Orders." Axioms 14, no. 2 (2025): 92. https://doi.org/10.3390/axioms14020092.

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In this paper, we focus on the existence and asymptotic estimates of the maximal and minimal solutions for a coupled tempered fractional differential system with different orders. By introducing an order reduction technique and some new growth conditions, we establish some new results on the existence of positive extremal solutions for the tempered fractional differential system, meanwhile, we also obtain the asymptotic estimate of the positive extreme solution by an iterative technique, which possesses a sharp asymptotic estimate. In particular, the iterative sequences converging to maximal a

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40

Cruz Ortega, Alonso, and Federico Menéndez-Conde Lara. "Maximal algebraic connectivity for paths with fixed total resistance." Pesquimat 26, no. 2 (2023): 11–24. http://dx.doi.org/10.15381/pesquimat.v26i2.24218.

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We consider the problem on finding the edge weights that maximize the algebraic connectivity of a graph, subject to the condition that the total resistance remains constant. For the paths P3 y P4 the solution to the problem is given. It is conjectured that for general graphs the solution is given for weights distributions that are invariant under graph automorphisms.

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41

Auzmendi, Jerónimo, Darío Fernández Do Porto, Carla Pallavicini, and Luciano Moffatt. "Achieving Maximal Speed of Solution Exchange for Patch Clamp Experiments." PLoS ONE 7, no. 8 (2012): e42275. http://dx.doi.org/10.1371/journal.pone.0042275.

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42

Baltz, Anthony J., Alfred Scharff Goldhaber, and Maurice Goldhaber. "Solar Neutrino Puzzle: An Oscillation Solution with Maximal Neutrino Mixing." Physical Review Letters 81, no. 26 (1998): 5730–33. http://dx.doi.org/10.1103/physrevlett.81.5730.

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43

Liu, Hai, Xiaowen Chu, Yiu-Wing Leung, Xiaohua Jia, and Peng-Jun Wan. "General Maximal Lifetime Sensor-Target Surveillance Problem and Its Solution." IEEE Transactions on Parallel and Distributed Systems 22, no. 10 (2011): 1757–65. http://dx.doi.org/10.1109/tpds.2011.42.

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44

Darehmiraki, Majid. "A New Solution for Maximal Clique Problem based Sticker Model." Biosystems 95, no. 2 (2009): 145–49. http://dx.doi.org/10.1016/j.biosystems.2008.09.007.

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Kowalczyk, Michał, Angela Pistoia, and Giusi Vaira. "Maximal solution of the Liouville equation in doubly connected domains." Journal of Functional Analysis 277, no. 9 (2019): 2997–3050. http://dx.doi.org/10.1016/j.jfa.2019.06.013.

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46

Deb, Rajat, and Tae Kun Seo. "Maximal surplus from the pivotal mechanism: a closed form solution." Review of Economic Design 3, no. 4 (1998): 347–57. http://dx.doi.org/10.1007/s100580050020.

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47

Kalton, N. J., and G. Lancien. "A solution to the problem of $L^p-$maximal regularity." Mathematische Zeitschrift 235, no. 3 (2000): 559–68. http://dx.doi.org/10.1007/pl00004816.

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Li, Lin, Dongqing Su, and Xuejun Zhao. "An Iterative Algorithm for Maximal and Minimal Solutions of a Class Matrix Equations." Journal of Physics: Conference Series 2747, no. 1 (2024): 012006. http://dx.doi.org/10.1088/1742-6596/2747/1/012006.

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Abstract In the paper, the peak solutions of a class equation is studied, the peak solutions are the maximal and minimal solutions. There is an iterative algorithm given for the solutions of the class equation. First, the existence of the peak solutions of the class equations is obtained. Second, when the peak solutions exist, an iterative algorithm is established to converge to the peak solutions of the class equation. By an upper bound and a lower bound of the solutions of the equation solution as the initial matrix, the iterative algorithm of the paper converges to the peak solutions of the

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49

Wang, Changyou, Haiqiang Zhang, and Shu Wang. "Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative." Discrete Dynamics in Nature and Society 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/425408.

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This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.

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50

Hoa, Ngo Van, and Nguyen Dinh Phu. "On Maximal and Minimal Solutions for Set-Valued Differential Equations with Feedback Control." Abstract and Applied Analysis 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/816218.

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In this paper, we present the existence of extremal solutions of set-valued differential equations with feedback control on semilinear Hausdorff space under Hukuhara derivative which is developed under the formDHX(t)=F(t,X(t),H(t,X(t))),X(0)=X0, for all t∈[0,T]with the monotone iterative technique and we will verify that monotone sequence of approximate solutions converging uniformly to the solution of the problem, that is useful for optimization problems.

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