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

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.

Existence and Multiple Solutions for Higher Order Difference Dirichlet Boundary Value Problems

2018 ◽  
Vol 19 (5) ◽  
pp. 539-544
Author(s):  
Lianwu Yang
Keyword(s):  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Higher Order ◽  
Nonlinear Difference Equation ◽  
Linking Theorem ◽  
Order Difference ◽  
Existence And Multiplicity

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.

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

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.

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

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
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.

scholarly journals Existence of Solutions to Boundary Value Problems for the Discrete Generalized Emden-Fowler Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Tieshan He ◽  
Fengjian Yang
Keyword(s):  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Theory ◽  
Minimax Methods ◽  
Fowler Equation

We consider the existence of solutions to boundary value problems for the discrete generalized Emden-Fowler equation. By means of the minimax methods in the critical point theory, some new results are obtained. Two examples are also given to illustrate the main results.

scholarly journals Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1207
Author(s):  
Feng Xiong ◽  
Zhan Zhou
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Laplacian Operator

In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example.

scholarly journals ON WELL POSED IMPULSIVE BOUNDARY VALUE PROBLEMS FOR P(T)-LAPLACIAN'S

2013 ◽  
Vol 18 (2) ◽  
pp. 161-175
Author(s):  
Marek Galewski ◽  
Donal O'Regan
Keyword(s):  
Variational Methods ◽  
Critical Point Theory ◽  
Continuous Dependence ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Theory ◽  
Impulsive Boundary Value Problems ◽  
Impulsive Problems ◽  
Well Posed

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.

Sign in / Sign up

Export Citation Format

Share Document