Existence of Multiple Solutions for a Class ofn-Dimensional Discrete Boundary Value Problems

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2010/198465 ◽

2010 ◽

Vol 2010 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Weiming Tan ◽

Zhan Zhou

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Multiple Solutions ◽

Boundary Value ◽

Point Theory

By using critical point theory, we obtain some new results on the existence of multiple solutions for a class ofn-dimensional discrete boundary value problems. Results obtained extend or improve existing ones.

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Solutions to discrete multiparameter periodic boundary value problems involving the p-laplacian via critical point theory

Acta Mathematica Scientia ◽

10.1016/s0252-9602(14)60081-3 ◽

2014 ◽

Vol 34 (4) ◽

pp. 1225-1236 ◽

Cited By ~ 4

Author(s):

Chenghua GAO

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Periodic Boundary ◽

Boundary Value ◽

Point Theory ◽

Periodic Boundary Value Problems

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Solvability of Boundary Value Problems for Impulsive Fractional Differential Equations Via Critical Point Theory

Mediterranean Journal of Mathematics ◽

10.1007/s00009-016-0779-4 ◽

2016 ◽

Vol 13 (6) ◽

pp. 4845-4866 ◽

Cited By ~ 5

Author(s):

Yanning Wang ◽

Yongkun Li ◽

Jianwen Zhou

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Critical Point ◽

Fractional Differential Equations ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Impulsive Fractional Differential Equations ◽

Fractional Differential

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Existence and multiple solutions for a second-order difference boundary value problem via critical point theory

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.03.017 ◽

2007 ◽

Vol 326 (1) ◽

pp. 511-520 ◽

Cited By ~ 54

Author(s):

Haihua Liang ◽

Peixuan Weng

Keyword(s):

Boundary Value Problem ◽

Critical Point ◽

Critical Point Theory ◽

Multiple Solutions ◽

Boundary Value ◽

Point Theory ◽

Second Order ◽

Order Difference

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Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues

Communications in Partial Differential Equations ◽

10.1080/03605308508820374 ◽

1985 ◽

Vol 10 (2) ◽

pp. 107-150 ◽

Cited By ~ 25

Author(s):

A.C. Lazer ◽

P.J. McKenna

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Multiple Eigenvalues

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Existence of the Solutions for a Class of Nonlinear Difference Systems Boundary Value Problem

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.281.312 ◽

2013 ◽

Vol 281 ◽

pp. 312-318

Author(s):

Fang Su ◽

Xue Wen Qin

Keyword(s):

Boundary Value Problem ◽

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Difference Systems

In this paper, by using critical point theory, we obtain a new result on the existence of the solutions for a class of difference systems boundary value problems. Results obtained extend or improve existing ones.

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Multiple Solutions for Boundary Value Problems of p-Laplacian Difference Equations Containing Both Advance and Retardation

Mathematical Problems in Engineering ◽

10.1155/2020/8342735 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Zhenguo Wang ◽

Zhan Zhou

Keyword(s):

Boundary Value Problems ◽

Difference Equations ◽

Critical Point Theory ◽

Multiple Solutions ◽

Dirichlet Boundary ◽

Existence Of Solutions ◽

Boundary Value ◽

Open Interval ◽

Point Theory ◽

Infinitely Many Solutions

This paper concerns the existence of solutions for the Dirichlet boundary value problems of p-Laplacian difference equations containing both advance and retardation depending on a parameter λ. Under some suitable assumptions, infinitely many solutions are obtained when λ lies in a given open interval. The approach is based on the critical point theory.

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TWO POSITIVE SOLUTIONS OF SOME SINGULAR BOUNDARY VALUE PROBLEMS

Analysis and Applications ◽

10.1142/s0219530510001618 ◽

2010 ◽

Vol 08 (03) ◽

pp. 305-314 ◽

Cited By ~ 4

Author(s):

RADU PRECUP

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Positive Solutions ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Singular Boundary ◽

Singular Boundary Value Problems

The existence of two positive solutions for a class of singular boundary value problems is established by means of a combination of the Leray–Schauder principle with techniques from critical point theory.

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Existence of solutions for a class of fractional boundary value problems via critical point theory

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2011.03.086 ◽

2011 ◽

Vol 62 (3) ◽

pp. 1181-1199 ◽

Cited By ~ 111

Author(s):

Feng Jiao ◽

Yong Zhou

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Existence Of Solutions ◽

Boundary Value ◽

Point Theory ◽

Fractional Boundary Value Problems

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Solutions for discretep-Laplacian periodic boundary value problems via critical point theory

The Journal of Difference Equations and Applications ◽

10.1080/10236198.2010.491825 ◽

2012 ◽

Vol 18 (3) ◽

pp. 345-355 ◽

Cited By ~ 10

Author(s):

Li-Hua Bian ◽

Hong-Rui Sun ◽

Quan-Guo Zhang

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Periodic Boundary ◽

Boundary Value ◽

Point Theory ◽

Periodic Boundary Value Problems

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Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Difference Systems

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0138 ◽

2018 ◽

Vol 19 (5) ◽

pp. 531-537

Author(s):

Tao Zhou ◽

Xia Liu ◽

Haiping Shi

Keyword(s):

Boundary Value Problems ◽

Critical Point ◽

Critical Point Theory ◽

Existence Of Solutions ◽

Boundary Value ◽

Point Theory ◽

Mountain Pass Lemma ◽

Variational Technique ◽

Difference Systems ◽

Existence Criteria

AbstractThis paper is devoted to investigate a question of the existence of solutions to boundary value problems for a class of nonlinear difference systems. The proof is based on the notable mountain pass lemma in combination with variational technique. By using the critical point theory, some new existence criteria are obtained.

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