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Journal articles on the topic 'Upper and lower solution'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Ejraei, Ayoub, Samira Shirvani, Mohammad Ali Aroon, Milad Asgarpour Khansary, and Sepideh Khalaj. "Lower and upper critical solution temperatures of binary polymeric solutions." Fluid Phase Equilibria 425 (October 2016): 465–84. http://dx.doi.org/10.1016/j.fluid.2016.06.036.

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2

O'Regan, Donal, and Ravi P. Agarwal. "Singular Problems: An Upper and Lower Solution Approach." Journal of Mathematical Analysis and Applications 251, no. 1 (2000): 230–50. http://dx.doi.org/10.1006/jmaa.2000.7043.

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3

Liolios, A. A. "Upper and lower solution estimates in unilateral viscoelastodynamics." Acta Mechanica 66, no. 1-4 (1987): 275–78. http://dx.doi.org/10.1007/bf01184300.

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4

Zhang, Li, Xiankai Huang, and Weigao Ge. "Positive Solutions of Sturm-Liouville Boundary Value Problems in Presence of Upper and Lower Solutions." International Journal of Differential Equations 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/383294.

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We consider a kind of Sturm-Liouville boundary value problems. Using variational techniques combined with the methods of upper-lower solutions, the existence of at least one positive solution is established. Moreover, the upper solution and the lower solution are presented.

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5

Vrábeľ, Róbert. "Upper and lower solutions for singularly perturbed semilinear Neumann's problem." Mathematica Bohemica 122, no. 2 (1997): 175–80. http://dx.doi.org/10.21136/mb.1997.125912.

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6

Cabada, Alberto, and Lucía López-Somoza. "Lower and Upper Solutions for Even Order Boundary Value Problems." Mathematics 7, no. 10 (2019): 878. http://dx.doi.org/10.3390/math7100878.

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In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary conditions. We consider Neumann, Dirichlet, mixed and periodic boundary conditions.

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7

Blodgett, Robert J. "Upper and Lower Bounds for a Serial Dilution Test." Journal of AOAC INTERNATIONAL 88, no. 4 (2005): 1227–30. http://dx.doi.org/10.1093/jaoac/88.4.1227.

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Abstract A Poisson-binomial model estimates the concentration of a target microbe from a serial dilution test. The maximum likelihood procedure gives an equation whose solution equals the estimate of the concentration. This paper gives bounds for the solution to this equation that require only minimal calculations.

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8

Grasso, F., and M. Marini. "Lower upper implicit total variation diminishing solution of viscoushypersonic flows." AIAA Journal 30, no. 9 (1992): 2184–85. http://dx.doi.org/10.2514/3.11202.

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9

Moelbert, Susanne, and Paolo De Los Rios. "Hydrophobic Interaction Model for Upper and Lower Critical Solution Temperatures." Macromolecules 36, no. 15 (2003): 5845–53. http://dx.doi.org/10.1021/ma025890c.

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10

Kim, Chul, S. Y. Jung, and J. C. Choi. "A lower upper-bound solution for shear spinning of cones." International Journal of Mechanical Sciences 45, no. 11 (2003): 1893–911. http://dx.doi.org/10.1016/j.ijmecsci.2003.11.002.

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11

Chamberlain,, J. A., D. J. Horrobin,, K. A. Landman, and, and J. E. Sader. "Upper and Lower Bounds for Incipient Failure in a Body Under Gravitational Loading." Journal of Applied Mechanics 71, no. 4 (2004): 586–89. http://dx.doi.org/10.1115/1.1767164.

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Recent numerical work has investigated incipient failure of yield stress materials under gravitational loading, for both the rectangular block and cylinder geometries [Chamberlain et al.; 2001, Int. J. Mech. Sci. 43(3):793-815, 2002, Int. J. Mech. Sci. 44(8):1779-1800]. While the rectangular block solution is exact, the cylinder solutions give lower bounds on the height of incipient failure. Consequently, we construct upper bound solutions for the height of incipient failure of a cylinder under gravitational loading. This closes the cylinder problem and quantifies the accuracy of the Haar-Karm

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12

Yang, Dandan, and Chuanzhi Bai. "Upper and Lower Solution Method for Fractional Boundary Value Problems on the Half-Line." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/349025.

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We establish the existence of unbounded solutions for nonlinear fractional boundary value problems on the half-line. By the upper and lower solution method technique, sufficient conditions for the existence of solutions for the fractional boundary value problems are established. An example is presented to illustrate our main result.

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13

Hu, Chaozhu, Bin Liu, and Songfa Xie. "Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/493164.

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By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.

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14

Wong, Patricia J. Y., and Ravi P. Agarwal. "Upper and Lower Solutions Method for A System of Higher Order Difference Equations." Georgian Mathematical Journal 7, no. 3 (2000): 585–98. http://dx.doi.org/10.1515/gmj.2000.585.

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Abstract Upper and lower solutions method is used to obtain the existence of a solution for the following system of boundary value problems: where ũi (k) = (ui (k), Δui (k), … , Δn–2 ui (k)), 1 ≤ i ≤ m.

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15

Chen, Guoping, and Jianhua Shen. "Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations." gmj 16, no. 4 (2009): 617–28. http://dx.doi.org/10.1515/gmj.2009.617.

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Abstract This paper is concerned with the existence of extreme solutions of nonlinear three-point boundary value problems for a class of first order impulsive functional differential equations. In the presence of a lower solution α and an upper solution β with the classical condition α ≤ β or the reversed ordering condition β ≤ α, some sufficient conditions for the existence of extreme solutions are obtained by using the method of upper and lower solutions coupled with the monotone iterative technique.

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16

Cabada, Alberto. "The method of lower and upper solutions for n th-order periodic boundary value problems." Journal of Applied Mathematics and Stochastic Analysis 7, no. 1 (1994): 33–47. http://dx.doi.org/10.1155/s1048953394000043.

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In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(n)(t)=f(t,u(t));u(i)(a)−u(i)(b)=λi∈ℝ,i=0,…,n−1 where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n≥3 with either α≤β or α≥β.For this, we study some maximum principles for the operator Lu≡u(n)+Mu. Furthermore, we obtain a generalization of the method of mixed monotonicity considering f and u as vectorial functions.

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17

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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18

Ding, Youzheng, and Zhongli Wei. "On the extremal solution for a nonlinear boundary value problems of fractional p-Laplacian differential equation." Filomat 30, no. 14 (2016): 3771–78. http://dx.doi.org/10.2298/fil1614771d.

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This paper is concerned with the existence and uniqueness of extremal solution for a nonlinear boundary value problems of fractional differential equation involving Riemann-Liouville derivative and p-Laplacian operator. By applying monotone iterative technique and lower and upper solutions method, we obtain sufficient conditions for the existence and uniqueness of extremal solution and construct the sequences of iteration to approximate it. The paper extends the applications of lower and upper solutions method and obtains some new results.

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19

Ortega, Rafael, and Massimo Tarallo. "Almost periodic upper and lower solutions." Journal of Differential Equations 193, no. 2 (2003): 343–58. http://dx.doi.org/10.1016/s0022-0396(03)00130-x.

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20

Liz, Eduardo, and Rodrigo L. Pouso. "Upper and Lower Solutions with “Jumps”." Journal of Mathematical Analysis and Applications 222, no. 2 (1998): 484–93. http://dx.doi.org/10.1006/jmaa.1998.5945.

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21

YU, XIAOJING, CHUFEN WU, and PEIXUAN WENG. "TRAVELING WAVES FOR A SIRS MODEL WITH NONLOCAL DIFFUSION." International Journal of Biomathematics 05, no. 05 (2012): 1250036. http://dx.doi.org/10.1142/s1793524511001787.

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In this paper, we study a delayed SIRS model with nonlocal diffusion. The well posedness of the model is investigated. Furthermore, we concern with the problem of traveling wave solutions. By using the partial quasi-monotone condition, cross-iteration scheme and fixed-point theorem, sufficient conditions are derived for the existence of traveling waves connecting the two equilibria which depends on the existence of a pair of upper solution and lower solution. We in fact construct a pair of upper solution and lower solution concretely to guarantee the existence of traveling waves.

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22

Agarwal, R. P., Donal O'Regan, V. Lakshmikantham, and S. Leela. "An upper and lower solution theory for singular Emden–Fowler equations." Nonlinear Analysis: Real World Applications 3, no. 2 (2002): 275–91. http://dx.doi.org/10.1016/s1468-1218(01)00029-3.

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23

Al Mosa, Samerah, and Paul Eloe. "Upper and lower solution method for boundary value problems at resonance." Electronic Journal of Qualitative Theory of Differential Equations, no. 40 (2016): 1–13. http://dx.doi.org/10.14232/ejqtde.2016.1.40.

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24

Wang, Chengwen. "Generalized upper and lower solution method for the forced Duffing equation." Proceedings of the American Mathematical Society 125, no. 2 (1997): 397–406. http://dx.doi.org/10.1090/s0002-9939-97-03947-6.

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25

Ehme, Jeffrey, Paul W. Eloe, and Johnny Henderson. "Upper and Lower Solution Methods for Fully Nonlinear Boundary Value Problems." Journal of Differential Equations 180, no. 1 (2002): 51–64. http://dx.doi.org/10.1006/jdeq.2001.4056.

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26

Delmas, G., and D. Patterson. "The molecular weight dependence of lower and upper critical solution temperatures." Journal of Polymer Science Part C: Polymer Symposia 30, no. 1 (2007): 1–8. http://dx.doi.org/10.1002/polc.5070300103.

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27

Mori, Hideharu, Ikumi Kato, Shoko Saito, and Takeshi Endo. "Proline-Based Block Copolymers Displaying Upper and Lower Critical Solution Temperatures." Macromolecules 43, no. 3 (2010): 1289–98. http://dx.doi.org/10.1021/ma902002b.

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28

Cong, Guangmin, Yuhui Huang, William J. MacKnight, and Frank E. Karasz. "Upper and lower critical solution temperature behavior in thermoplastic polymer blends." Macromolecules 19, no. 11 (1986): 2765–70. http://dx.doi.org/10.1021/ma00165a018.

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29

Nefedov, Nikolay. "The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection." Mathematical Modelling of Natural Phenomena 14, no. 4 (2019): 401. http://dx.doi.org/10.1051/mmnp/2019009.

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We consider a new class of singularly perturbed parabolic periodic boundary value problems for reaction-advection-diffusion equations: Burgers type equations with modular advection. We construct the interior layer type formal asymptotics and propose a modified procedure to get asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. The asymptotic stability of this solution is also established.

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30

Karlstroem, Gunnar. "A new model for upper and lower critical solution temperatures in poly(ethylene oxide) solutions." Journal of Physical Chemistry 89, no. 23 (1985): 4962–64. http://dx.doi.org/10.1021/j100269a015.

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31

Habets, Patrick, and Rodrigo L. Pouso. "Examples of the nonexistence of a solution in the presence of upper and lower solutions." ANZIAM Journal 44, no. 4 (2003): 591–94. http://dx.doi.org/10.1017/s1446181100012955.

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AbstractStandard results for boundary value problems involving second-order ordinary differential equations ensure that the existence of a well-ordered pair of lower and upper solutions together with a Nagumo condition imply existence of a solution. In this note we introduce some examples which show that existence is not guaranteed if no Nagumo condition is satisfied.

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32

GEMMA, Tohru, and Kazuyoshi OGINO. "Light scattering for Polystyrene solutions in cyclopentane near the upper and lower critical solution points." KOBUNSHI RONBUNSHU 44, no. 8 (1987): 621–29. http://dx.doi.org/10.1295/koron.44.621.

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33

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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34

Al-Refai, Mohammed, and Qutaibeh Katatbeh. "Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–13. http://dx.doi.org/10.1155/ijmms/2006/24391.

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Comparison arguments are used to study a problem in combustion theory consisting of a nonlinear parabolic equation together with initial and boundary conditions. Upper and lower bounds for the problem are constructed. The lower solutions are used to determine whether the solution of the problem is increasing in time for certain initial condition. Numerical results are presented for the slab, infinite cylinder, and unit sphere. The bounds are compared with the existing ones in the literature for the slab geometry.

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35

Liu, Xinzhi. "Nonlinear boundary value problems for first order impulsive integro-differential equations." Journal of Applied Mathematics and Simulation 2, no. 3 (1989): 185–98. http://dx.doi.org/10.1155/s1048953389000146.

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In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.

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36

Lin, Jian-Jhong, and Ting-Hui Yang. "Traveling wave solutions for a diffusive three-species intraguild predation model." International Journal of Biomathematics 11, no. 02 (2018): 1850022. http://dx.doi.org/10.1142/s1793524518500225.

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The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper–lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper–lower solution, the scheme of strictly contracting rectangle is applied. Finally, the minimal speed [Formula: see text] of traveling wave solutions of the model is characterized. If the wave speed is

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37

Goyal, Vandana, Namrata Rani, and Deepak Gupta. "Iterative Parametric Approach for Quadratically Constrained Bi-Level Multiobjective Quadratic Fractional Programming." Journal of Computational and Theoretical Nanoscience 17, no. 11 (2020): 5046–51. http://dx.doi.org/10.1166/jctn.2020.9339.

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The paper proposed an iterative parametric approach procedure for solving Bi-level Multiobjective Quadratic Fractional Programming model. The Model is divided into two levels-upper and lower. In the first stage of the approach, a set of pareto optimal solutions of upper Level is obtained by converting the problem into equivalent single non-fractional parametric objective optimization problem by using parametric vector and ε-constraint method. Then for the second stage, the solution of upper level is followed by the lower level decision maker while finding solution with the proposed algorithm t

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38

Wang, Yuan-Ming, and Ravi P. Agarwal. "Monotone methods for solving a boundary value problem of second order discrete system." Mathematical Problems in Engineering 5, no. 4 (1999): 291–315. http://dx.doi.org/10.1155/s1024123x99001106.

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A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

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39

Gao, Yongxin, and Fengqin Wang. "Existence of Solutions of Nonlinear Mixed Two-Point Boundary Value Problems for Third-Order Nonlinear Differential Equation." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/262139.

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The authors use the upper and lower solution method to study the existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equation y′′′=f(x,y,y′,y′′), y′(b)=h(y′(a)), p(y(a),y(b),y′(a),y′(b))=0, g(y(a),y(b),y′(a),y′(b),y′′(a),y′′(b))=0. Some new existence results are obtained by developing the upper and lower solution method. Some applications are also presented.

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40

Quilliot, Alain, Djamal Rebaine, and Hélène Toussaint. "Lower and upper bounds for the linear arrangement problem on interval graphs." RAIRO - Operations Research 52, no. 4-5 (2018): 1123–45. http://dx.doi.org/10.1051/ro/2017011.

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We deal here with theLinear Arrangement Problem(LAP) onintervalgraphs, any interval graph being given here together with its representation as theintersectiongraph of some collection of intervals, and so with relatedprecedenceandinclusionrelations. We first propose a lower boundLB, which happens to be tight in the case ofunit intervalgraphs. Next, we introduce the restriction PCLAP of LAP which is obtained by requiring any feasible solution of LAP to be consistent with theprecedencerelation, and prove that PCLAP can be solved in polynomial time. Finally, we show both theoretically and experime

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41

Darzi, R., B. Mohammadzadeh, A. Neamaty, and D. Bǎleanu. "Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/847184.

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We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problemD0+αut+ft,ut=0,0<t<1,2<α≤3,u0=u′0=0,D0+α−1u1=βuξ,0<ξ<1, whereD0+αdenotes Riemann-Liouville fractional derivative,βis positive real number,βξα−1≥2Γα, andfis continuous on0,1×0,∞. As an application, one example is given to illustrate the main result.

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42

Agarwal, R. P., D. O'Regan, V. Lakshmikantham, and S. Leela. "A generalized upper and lower solution method for singular initial value problems." Computers & Mathematics with Applications 47, no. 4-5 (2004): 739–50. http://dx.doi.org/10.1016/s0898-1221(04)90061-2.

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43

Cai, Xin, Liang Zhong, Yue Su, Shaoliang Lin, and Xiaohua He. "Novel pH-tunable thermoresponsive polymers displaying lower and upper critical solution temperatures." Polymer Chemistry 6, no. 20 (2015): 3875–84. http://dx.doi.org/10.1039/c5py00234f.

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44

De Coster, Colette. "Existence, localization, and instability of solution in presence of non-well-ordered lower and upper solutions." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 8 (1998): 935–40. http://dx.doi.org/10.1016/s0764-4442(98)80117-1.

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45

Berry, Guy C., Edward F. Casassa, and Pi-Yao Liu. "Polystyrene in cyclopentane: Dilute solution properties from the upper critical to the lower critical solution temperature." Journal of Polymer Science Part B: Polymer Physics 25, no. 3 (1987): 673–96. http://dx.doi.org/10.1002/polb.1987.090250317.

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46

Yang, Xiaojing. "Upper and lower solutions for periodic problems." Applied Mathematics and Computation 137, no. 2-3 (2003): 413–22. http://dx.doi.org/10.1016/s0096-3003(02)00147-9.

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47

Rachůnková, Irena. "Upper and Lower Solutions and Topological Degree." Journal of Mathematical Analysis and Applications 234, no. 1 (1999): 311–27. http://dx.doi.org/10.1006/jmaa.1999.6375.

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48

Rachůnková, Irena. "Upper and Lower Solutions and Multiplicity Results." Journal of Mathematical Analysis and Applications 246, no. 2 (2000): 446–64. http://dx.doi.org/10.1006/jmaa.2000.6798.

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49

Chu, Yu-Ming, Umair Khan, A. Zaib, S. H. A. M. Shah, and Marin Marin. "Numerical and Computer Simulations of Cross-Flow in the Streamwise Direction through a Moving Surface Comprising the Significant Impacts of Viscous Dissipation and Magnetic Fields: Stability Analysis and Dual Solutions." Mathematical Problems in Engineering 2020 (September 29, 2020): 1–11. http://dx.doi.org/10.1155/2020/8542396.

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The inspiration for this study is to explore the crucial impact of viscous dissipation (VISD) on magneto flow through a cross or secondary flow (CRF) in the way of streamwise. Utilizing the pertinent similarity method, the primary partial differential equations (PDEs) are changed into a highly nonlinear dimensional form of ordinary differential equations (ODEs). These dimensionless forms of ODEs are executed numerically by the aid of bvp4c solver. The impact of pertinent parameters such as the suction parameter, magnetic parameter, moving parameter, and viscous dissipation parameter is discuss

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50

Verma, Amit K., Nazia Urus, and Mandeed Singh. "Monotone Iterative Technique for a Class of Four Point BVPs with Reversed Ordered Upper and Lower Solutions." International Journal of Computational Methods 17, no. 09 (2019): 1950066. http://dx.doi.org/10.1142/s021987621950066x.

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Consider the class of four point nonlinear BVPs [Formula: see text] [Formula: see text] where [Formula: see text] is continuous, [Formula: see text], [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, we demonstrate an iterative technique. The iterative scheme is deduced by using quasilinearization. Then we consider upper-lower solutions in well ordered and reverse ordered cases and prove existence of solutions under some sufficient conditions. We show that under certain conditions, generated sequences are monotone, uniformly convergent and converges to t

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