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Journal articles on the topic 'Variational critical problems'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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1

Ambrosetti, Antonio. "Critical points and nonlinear variational problems." Mémoires de la Société mathématique de France 1 (1992): 1–139. http://dx.doi.org/10.24033/msmf.362.

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2

Prigozhin, Leonid. "Variational inequalities in critical-state problems." Physica D: Nonlinear Phenomena 197, no. 3-4 (2004): 197–210. http://dx.doi.org/10.1016/j.physd.2004.07.001.

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3

Prigozhin, L. "On the Bean critical-state model in superconductivity." European Journal of Applied Mathematics 7, no. 3 (1996): 237–47. http://dx.doi.org/10.1017/s0956792500002333.

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We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

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4

Leonardi, Salvatore, and Nikolaos S. Papageorgiou. "On a class of critical Robin problems." Forum Mathematicum 32, no. 1 (2020): 95–109. http://dx.doi.org/10.1515/forum-2019-0160.

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AbstractWe consider a nonlinear parametric Robin problem. In the reaction, there are two terms, one critical and the other locally defined. Using cut-off techniques, together with variational tools and critical groups, we show that, for all small values of the parameter, the problem has at least three nontrivial smooth solutions all with sign information, which converge to zero in {C^{1}(\bar{\Omega})} as the parameter {\lambda\to 0^{+}}.

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5

Stupishin, Leonid U. "Variational Criteria for Critical Levels of Internal Energy of a Deformable Solids." Applied Mechanics and Materials 578-579 (July 2014): 1584–87. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.1584.

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Variational formulation of the problem of the analysis and synthesis of deformable structures are proposed. It allows studying nonlinear problems of structural mechanics from a single standpoint, from a consideration of the General variational principle.

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6

Ambrosetti, A., J. Garcia Azorero, and I. Peral. "Elliptic Variational Problems in RN with Critical Growth." Journal of Differential Equations 168, no. 1 (2000): 10–32. http://dx.doi.org/10.1006/jdeq.2000.3875.

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7

Hammouti, Omar, Said Taarabti, and Ravi Agarwal. "Anisotropic discrete boundary value problems." Applicable Analysis and Discrete Mathematics, no. 00 (2023): 8. http://dx.doi.org/10.2298/aadm220824008h.

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For an anisotropic discrete nonlinear problem with variable exponent, we demonstrate both the existence and multiplicity of nontrivial solutions in this study. The variational principle and critical point theory are the key techniques employed here.

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8

Gazzola, Filippo. "Positive solutions of critical quasilinear elliptic problems in general domains." Abstract and Applied Analysis 3, no. 1-2 (1998): 65–84. http://dx.doi.org/10.1155/s108533759800044x.

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We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

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9

Li, Lin, and Stepan Tersian. "Fractional problems with critical nonlinearities by a sublinear perturbation." Fractional Calculus and Applied Analysis 23, no. 2 (2020): 484–503. http://dx.doi.org/10.1515/fca-2020-0023.

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AbstractIn this paper, the existence of two nontrivial solutions for a fractional problem with critical exponent, depending on real parameters, is established. The variational approach is used based on a local minimum theorem due to G. Bonanno. In addition, a numerical estimate on the real parameters is provided, for which the two solutions are obtained.

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10

Drissi, Amor, Abdeljabbar Ghanmi, and Dusan D. Repovs. "Singular p-biharmonic problems involving the Hardy-Sobolev exponent." Electronic Journal of Differential Equations 2023, no. 01-?? (2023): 61. http://dx.doi.org/10.58997/ejde.2023.61.

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This article concerns the existence and multiplicity of solutions for the singular p-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. To this end we use variational methods combined with the Mountain pass theorem and the Ekeland variational principle. We illustrate the usefulness of our results with and example. For mote information see https://ejde.math.txstate.edu/Volumes/2023/61/abstr.html

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11

Kang, Dongsheng. "Quasilinear elliptic problems with critical exponents and Hardy terms in ℝN". Proceedings of the Edinburgh Mathematical Society 53, № 1 (2010): 175–93. http://dx.doi.org/10.1017/s0013091508000187.

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AbstractWe deal with a singular quasilinear elliptic problem, which involves critical Hardy-Sobolev exponents and multiple Hardy terms. Using variational methods and analytic techniques, the existence of ground state solutions to the problem is obtained.

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12

Lian, Chun-Bo, Bei-Lei Zhang, and Bin Ge. "Multiple Solutions for Double Phase Problems with Hardy Type Potential." Mathematics 9, no. 4 (2021): 376. http://dx.doi.org/10.3390/math9040376.

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In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity f. Here we use Ricceri’s variational principle and Bonanno’s three critical points theorem in order to overcome the lack of compactness.

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13

Ghoussoub, Nassif, and Frédéric Robert. "Hardy-singular boundary mass and Sobolev-critical variational problems." Analysis & PDE 10, no. 5 (2017): 1017–79. http://dx.doi.org/10.2140/apde.2017.10.1017.

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14

Chow, Shui-Nee, and Reiner Lauterbach. "A bifurcation theorem for critical points of variational problems." Nonlinear Analysis: Theory, Methods & Applications 12, no. 1 (1988): 51–61. http://dx.doi.org/10.1016/0362-546x(88)90012-0.

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15

Chen, Yu. "G-α-preinvex functions and non-smooth vector optimization problems". Yugoslav Journal of Operations Research, № 00 (2021): 8. http://dx.doi.org/10.2298/yjor200527008c.

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In this paper, we proposed the non-smooth G-?-preinvexity by generalizing ?-invexity and G-preinvexity, and discussed some solution properties about non-smooth vector optimization problems and vector variational-like inequality problems under the condition of non-smooth G-?-preinvexity. Moreover, we also proved that the vector critical points, the weakly efficient points and the solutions of the non-smooth weak vector variational-like inequality problem are equivalent under non-smooth pseudo-G-?-preinvexity assumptions.

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16

Khodabakhshi, Mehdi, Abdolmohammad Aminpour, and Mohamad Tavani. "Infinitely many weak solutions for some elliptic problems in RN." Publications de l'Institut Math?matique (Belgrade) 100, no. 114 (2016): 271–78. http://dx.doi.org/10.2298/pim1614271k.

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17

Liu, Shibo. "Multiple solutions for elliptic resonant problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 138, no. 6 (2008): 1281–89. http://dx.doi.org/10.1017/s0308210507000443.

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Two non-trivial solutions for semilinear elliptic resonant problems are obtained via the Lyapunov—Schmidt reduction and the three-critical-points theorem. The difficulty that the variational functional does not satisfy the Palais—Smale condition is overcome by taking advantage of the reduction and a careful analysis of the reduced functional.

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18

Wei, Yongfang, Suiming Shang, and Zhanbing Bai. "Applications of variational methods to some three-point boundary value problems with instantaneous and noninstantaneous impulses." Nonlinear Analysis: Modelling and Control 27 (February 4, 2022): 1–13. http://dx.doi.org/10.15388/namc.2022.27.26253.

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In this paper, we study the multiple solutions for some second-order p-Laplace differential equations with three-point boundary conditions and instantaneous and noninstantaneous impulses. By applying the variational method and critical point theory the multiple solutions are obtained in a Sobolev space. Compared with other local boundary value problems, the three-point boundary value problem is less studied by variational method due to its variational structure. Finally, two examples are given to illustrate the results of multiplicity.

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19

Ribeiro, Bruno. "Critical elliptic problems in ℝ2 involving resonance in high-order eigenvalues". Communications in Contemporary Mathematics 17, № 01 (2014): 1450008. http://dx.doi.org/10.1142/s0219199714500084.

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In this paper we deal with the following class of problems [Formula: see text] where Ω ⊂ ℝ2 is bounded with smooth boundary, g has a unilateral critical behavior of Trudinger–Moser type and λk denotes the kth eigenvalue of [Formula: see text], k ≥ 2. We prove existence of nontrivial solution for this problem using variational methods.

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20

Béhi, Droh Arsène, and Assohoun Adjé. "A Variational Method for Multivalued Boundary Value Problems." Abstract and Applied Analysis 2020 (January 21, 2020): 1–8. http://dx.doi.org/10.1155/2020/8463263.

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In this paper, we investigate the existence of solution for differential systems involving a ϕ−Laplacian operator which incorporates as a special case the well-known p−Laplacian operator. In this purpose, we use a variational method which relies on Szulkin’s critical point theory. We obtain the existence of solution when the corresponding Euler–Lagrange functional is coercive.

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21

Kyritsi, Sophia Th, and Nikolaos S. Papageorgiou. "Multiple Solutions for Nonlinear Periodic Problems." Canadian Mathematical Bulletin 56, no. 2 (2013): 366–77. http://dx.doi.org/10.4153/cmb-2011-154-5.

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Abstract We consider a nonlinear periodic problem driven by a nonlinear nonhomogeneous differential operator and a Carathéodory reaction term f (t; x) that exhibits a (p – 1)-superlinear growth in x 2 R near 1 and near zero. A special case of the differential operator is the scalar p-Laplacian. Using a combination of variational methods based on the critical point theory with Morse theory (critical groups), we show that the problem has three nontrivial solutions, two of which have constant sign (one positive, the other negative).

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22

Kaid, Rachida, Atika Matallah, and Sofiane Messirdi. "Multiple solutions to p-Kirchhoff type problems involving critical Sobolev exponent in R^N." MATHEMATICA 65 (88), no. 1 (2023): 75–84. http://dx.doi.org/10.24193/mathcluj.2023.1.08.

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23

Yang, Dianwu. "A Variational Principle for Three-Point Boundary Value Problems with Impulse." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/840408.

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We construct a variational functional of a class of three-point boundary value problems with impulse. Using the critical points theory, we study the existence of solutions to second-order three-point boundary value problems with impulse.

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24

Galewski, Marek, and Donal O'Regan. "ON WELL POSED IMPULSIVE BOUNDARY VALUE PROBLEMS FOR P(T)-LAPLACIAN'S." Mathematical Modelling and Analysis 18, no. 2 (2013): 161–75. http://dx.doi.org/10.3846/13926292.2013.779600.

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In this paper we investigate via variational methods and critical point theory the existence of solutions, uniqueness and continuous dependence on parameters to impulsive problems with a p(t)-Laplacian and Dirichlet boundary value conditions.

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25

Alves, C. O., Ana Maria Bertone, and J. V. Goncalves. "A Variational Approach to Discontinuous Problems with Critical Sobolev Exponents." Journal of Mathematical Analysis and Applications 265, no. 1 (2002): 103–27. http://dx.doi.org/10.1006/jmaa.2001.7698.

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26

Mishra, S. K., and Vivek Laha. "On V-r-invexity and vector variational-like inequalities." Filomat 26, no. 5 (2012): 1065–73. http://dx.doi.org/10.2298/fil1205065m.

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In this paper, we consider the multiobjective optimization problems involving the differentiable V-r-invex vector valued functions. Under the assumption of V-r-invexity, we use the Stampacchia type vector variational-like inequalities as tool to solve the vector optimization problems. We establish equivalence among the vector critical points, the weak efficient solutions and the solutions of the Stampacchia type weak vector variational-like inequality problems using Gordan?s separation theorem under the V-r-invexity assumptions. These conditions are more general than those appearing in the lit

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27

Shibata, Tetsutaro. "Asymptotic formulas and critical exponents for two-parameter nonlinear eigenvalue problems." Abstract and Applied Analysis 2003, no. 11 (2003): 671–84. http://dx.doi.org/10.1155/s1085337503212045.

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We study the nonlinear two-parameter problem−u″(x)+λu(x)q=μu(x)p,u(x)>0,x∈(0,1),u(0)=u(1)=0. Here,1<q<pare constants andλ,μ>0are parameters. We establish precise asymptotic formulas with exact second term for variational eigencurveμ(λ)asλ→∞. We emphasize that the critical case concerning the decaying rate of the second term isp=(3q−1)/2and this kind of criticality is new for two-parameter problems.

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28

Alves, Claudianor O., Daniel C. de Morais Filho та Marco A. S. Souto. "Multiplicity of positive solutions for a class of problems with critical growth in ℝN". Proceedings of the Edinburgh Mathematical Society 52, № 1 (2009): 1–21. http://dx.doi.org/10.1017/s0013091507000028.

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AbstractUsing variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:where λ,β∈(0,∞), q∈(1,2*−1), 2*=2N/(N−2), N≥3, V,Z:ℝN→ℝ are continuous functions verifying some hypotheses.

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29

Badiale, Marino, and Alessio Pomponio. "Bifurcation results for semilinear elliptic problems in RN." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 1 (2004): 11–32. http://dx.doi.org/10.1017/s0308210500003048.

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In this paper we obtain, for a semilinear elliptic problem in RN, families of solutions bifurcating from the bottom of the spectrum of −Δ. The problem is variational in nature and we apply a nonlinear reduction method that allows us to search for solutions as critical points of suitable functionals defined on finite-dimensional manifolds.

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30

Chen, Ching-yu, and Tsung-fang Wu. "Multiple positive solutions for indefinite semilinear elliptic problems involving a critical Sobolev exponent." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 4 (2014): 691–709. http://dx.doi.org/10.1017/s0308210512000133.

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In this paper, we study the decomposition of the Nehari manifold by exploiting the combination of concave and convex nonlinearities. The result is subsequently used, in conjunction with the Ljusternik–Schnirelmann category and variational methods, to prove the existence and multiplicity of positive solutions for an indefinite elliptic problem involving a critical Sobolev exponent.

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31

Shen, Yansheng. "Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities." Advanced Nonlinear Studies 21, no. 1 (2019): 77–93. http://dx.doi.org/10.1515/ans-2019-2056.

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Abstract In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝ N {\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential. Using variational methods, we investigate the attainability of the corresponding minimization problem, and then obtain the existence of solutions. We also consider another Choquard type equation involving the p-Laplacian and critical nonlinearities in ℝ N {\mathbb{R}^{N}} .

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32

Papageorgiou, Nikolaos S., Calogero Vetro, and Francesca Vetro. "Multiple solutions for semilinear Robin problems with superlinear reaction and no symmetries." Electronic Journal of Differential Equations 2021, no. 01-104 (2021): 12. http://dx.doi.org/10.58997/ejde.2021.12.

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We study a semilinear Robin problem driven by the Laplacian with a parametric superlinear reaction. Using variational tools from the critical point theory with truncation and comparison techniques, critical groups and flow invariance arguments, we show the existence of seven nontrivial smooth solutions, all with sign information and ordered. For more information see https://ejde.math.txstate.edu/Volumes/2021/12/abstr.html

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33

Carriao, Paulo Cesar, Augusto Cesar dos Reis Costa, Olimpio Hiroshi Miyagaki, and Andre Vicente. "Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space." Electronic Journal of Differential Equations 2021, no. 01-104 (2022): 3. http://dx.doi.org/10.58997/ejde.2021.53.

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In this work we study a class of the critical Kirchhoff-type problems in a Hyperbolic space Because of the Kirchhoff term, the nonlinearity \(u^q\) becomes concave for \(2<q<4\), This brings difficulties when proving the boundedness of Palais Smale sequences. We overcome this difficulty by using a scaled functional related with a Pohozaev manifold. In addition, we need to overcome singularities on the unit sphere, so that we use variational methods to obtain our results. For more information see https://ejde.math.txstate.edu/Volumes/2021/53/abstr.html

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34

Matallah, Atika, Safia Benmansour, and Hayat Benchira. "Existence and nonexistence of nontrivial solutions for a class of p-Kirchhoff type problems with critical Sobolev exponent." Filomat 36, no. 9 (2022): 2971–79. http://dx.doi.org/10.2298/fil2209971m.

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35

Ruiz-Garzón, Gabriel, Rafaela Osuna-Gómez, Antonio Rufián-Lizana, and Beatriz Hernández-Jiménez. "Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities." Mathematics 8, no. 12 (2020): 2196. http://dx.doi.org/10.3390/math8122196.

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This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated them with examples. We see the minimum requirements under which critical points, solutions of Stampacchia, and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results fro

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36

Papageorgiou, Nikolaos S., and Vicenţiu D. Rădulescu. "Semilinear Robin problems resonant at both zero and infinity." Forum Mathematicum 30, no. 1 (2018): 237–51. http://dx.doi.org/10.1515/forum-2016-0264.

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Abstract We consider a semilinear elliptic problem, driven by the Laplacian with Robin boundary condition. We consider a reaction term which is resonant at {\pm\infty} and at 0. Using variational methods and critical groups, we show that under resonance conditions at {\pm\infty} and at zero the problem has at least two nontrivial smooth solutions.

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37

Belaouidel, Hassan, Mustapha Haddaoui, and Najib Tsouli. "Results of singular Direchelet problem involving the $p(x)$-laplacian with critical growth." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–18. http://dx.doi.org/10.5269/bspm.52984.

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In this paper, we study the existence and multiplicity of solutions for Dirichlet singular elliptic problems involving the $p(x)$-Laplace equation with critical growth. The technical approach is mainly based on the variational method combined with the genus theory.

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38

Piccione, Paolo, and Daniel V. Tausk. "Lagrangian and Hamiltonian formalism for constrained variational problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 6 (2002): 1417–37. http://dx.doi.org/10.1017/s0308210500002183.

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We consider solutions of Lagrangian variational problems with linear constraints on the derivative. More precisely, given a smooth distribution D ⊂ TM on M and a time-dependent Lagrangian L defined on D, we consider an action functional L defined on the set ΩPQ(M, D) of horizontal curves in M connecting two fixed submanifolds P, Q ⊂ M. Under suitable assumptions, the set ΩPQ(M, D) has the structure of a smooth Banach manifold and we can thus study the critical points of L. If the Lagrangian L satisfies an appropriate hyper-regularity condition, we associate to it a degenerate Hamiltonian H on

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39

Borysiuk, Viktor, and Olha Michuta. "Application of Quantum Computing in Optimization Problems." Modeling, Control and Information Technologies, no. 7 (December 7, 2024): 123–24. https://doi.org/10.31713/mcit.2024.033.

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The article examines methods for applying quantum computing to solve optimization problems, which are critical in various fields such as logistics, finance, resource management, energy, and others. The potential of quantum algorithms, such as Grover's algorithm and Variational Quantum Algorithms (VQA), is explored for enhancing computational efficiency compared to classical methods. Quantum computing enables significant acceleration of optimal solution search processes and reduces the complexity of problems through parallel computing and quantum superposition.

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40

El Mokhtar, M. E. O., S. Benmansour, and A. Matallah. "On Nonlocal Elliptic Problems of the Kirchhoff Type Involving the Hardy Potential and Critical Nonlinearity." Journal of Applied Mathematics 2023 (August 24, 2023): 1–6. http://dx.doi.org/10.1155/2023/2997093.

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In this article, we deal with the nonlocal elliptic problems of the Kirchhoff type involving the Hardy potential and critical nonlinearity on a bounded domain in R 3 . Under an appropriate condition on the nonhomogeneous term and using variational methods, we obtain two distinct solutions.

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41

OUERGHI, HAIKEL, KHALD BENALI, and AMOR DRISSI. "EXISTENCE OF SOLUTIONS FOR NONHOMOGENEOUS DIRICHLET PROBLEMS IN ORLICZ-SOBOLEV SPACES." Journal of Science and Arts 24, no. 4 (2024): 881–94. https://doi.org/10.46939/j.sci.arts-24.4-a11.

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In this paper, by using variational methods and critical point theory in an appropriate Orlicz-Sobolev space, we establish the existence of infinitely many nontrivial solutions to a nonhomogeneous problem. Precisely, we use the Z_2-symmetric version for the well-known Mountain Pass theorem, to prove the existence of such solutions.

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42

Yang, Lianwu. "Existence and Multiple Solutions for Higher Order Difference Dirichlet Boundary Value Problems." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 5 (2018): 539–44. http://dx.doi.org/10.1515/ijnsns-2017-0176.

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AbstractIn this paper, a higher order nonlinear difference equation is considered. By using the critical point theory, we obtain the existence and multiplicity for solutions of difference Dirichlet boundary value problems and give some new results. The proof is based on the variational methods and linking theorem.

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43

Wysocki, K. "Multiple critical points for variational problems on partially ordered Hilbert spaces." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 7, no. 4 (1990): 287–304. http://dx.doi.org/10.1016/s0294-1449(16)30293-1.

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44

Liang, Sihua, Giovanni Molica Bisci, and Binlin Zhang. "Sign-changing solutions for Kirchhoff-type problems involving variable-order fractional Laplacian and critical exponents." Nonlinear Analysis: Modelling and Control 27 (March 28, 2022): 1–20. http://dx.doi.org/10.15388/namc.2022.27.26575.

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In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problem with critical variable exponent. By using constraint variational method and quantitative deformation lemma we show the existence of one least energy solution, which is strictly larger than twice of that of any ground state solution.

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45

AIZICOVICI, SERGIU, NIKOLAOS S. PAPAGEORGIOU, and VASILE STAICU. "NODAL AND MULTIPLE SOLUTIONS FOR NONLINEAR PERIODIC PROBLEMS WITH COMPETING NONLINEARITIES." Communications in Contemporary Mathematics 15, no. 03 (2013): 1350001. http://dx.doi.org/10.1142/s0219199713500016.

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We consider a nonlinear periodic problem drive driven by a nonhomogeneous differential operator which incorporates as a special case the scalar p-Laplacian, and a reaction which exhibits the competition of concave and convex terms. Using variational methods based on critical point theory, together with suitable truncation techniques and Morse theory (critical groups), we establish the existence of five nontrivial solutions, two positive, two negative and the fifth nodal (sign-changing). In the process, we also prove some auxiliary results of independent interest.

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46

Hadjian, Armin, and Juan J. Nieto. "Existence of solutions of Dirichlet problems for one dimensional fractional equations." AIMS Mathematics 7, no. 4 (2022): 6034–49. http://dx.doi.org/10.3934/math.2022336.

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<abstract><p>We establish the existence of infinitely many solutions for some nonlinear fractional differential equations under suitable oscillating behaviour of the nonlinear term. These problems have a variational structure and we prove our main results by using a critical point theorem due to Ricceri.</p></abstract>

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47

Carl, Siegfried, and Dumitru Motreanu. "Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters." International Journal of Differential Equations 2010 (2010): 1–33. http://dx.doi.org/10.1155/2010/536236.

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The study of multiple solutions for quasilinear elliptic problems under Dirichlet or nonlinear Neumann type boundary conditions has received much attention over the last decades. The main goal of this paper is to present multiple solutions results for elliptic inclusions of Clarke's gradient type under Dirichlet boundary condition involving the -Laplacian which, in general, depend on two parameters. Assuming different structure and smoothness assumptions on the nonlinearities generating the multivalued term, we prove the existence of multiple constant-sign and sign-changing (nodal) solutions f

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48

Heidari Tavani, Mohammad Reza. "Existence Results for A Perturbed Fourth-Order Equation." Journal of the Indonesian Mathematical Society 23, no. 2 (2017): 55–65. http://dx.doi.org/10.22342/jims.23.2.498.55-65.

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‎The existence of at least three weak solutions for a class of perturbed‎‎fourth-order problems with a perturbed nonlinear term is investigated‎. ‎Our‎‎approach is based on variational methods and critical point theory‎.

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49

Abd, Ghazwa F., and Radhi A. Zaboon. "Approximate Solution of a Reduced-Type Index- k Hessenberg Differential-Algebraic Control System." Journal of Applied Mathematics 2021 (October 11, 2021): 1–13. http://dx.doi.org/10.1155/2021/9706255.

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This study focuses on developing an efficient and easily implemented novel technique to solve the index- k Hessenberg differential-algebraic equation (DAE) with input control. The implicit function theorem is first applied to solve the algebraic constraints of having unknown state differential variables to form a reduced state-space representation of an ordinary differential (control) system defined on smooth manifold with consistent initial conditions. The variational formulation is then developed for the reduced problem. A solution of the reduced problem is proven to be the critical point of

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Shokooh, Saeid, Ghasem A. Afrouzi, and John R. Graef. "Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces." Mathematica Slovaca 68, no. 4 (2018): 867–80. http://dx.doi.org/10.1515/ms-2017-0151.

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Abstract:

Abstract By using variational methods and critical point theory in an appropriate Orlicz-Sobolev setting, the authors establish the existence of infinitely many non-negative weak solutions to a non-homogeneous Neumann problem. They also provide some particular cases and an example to illustrate the main results in this paper.

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