scholarly journals Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Jianmin Guo ◽  
Caixia Guo
Keyword(s):  
Positive Integer ◽  
Boundary Value Problem ◽  
Critical Point Theory ◽  
Difference Operator ◽  
Boundary Value ◽  
Point Theory ◽  
Point Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Forward Difference

By using Morse theory, the critical point theory, and the character of , we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem subject to , where is a positive integer, is the forward difference operator defined by , and is continuous. In argument, Morse inequalities play an important role.

scholarly journals Existence and Multiplicity Results for A Fourth-Order Boundary Value Problem

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Nemat Nyamoradi ◽  
Mohamad Rasoul Hamidi
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Nonsmooth Critical Point Theory ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Nonsmooth Critical Point

Abstract In this paper we consider a class of a fourth-order boundary value problem. Using a variational method based on nonsmooth critical point theory, we prove the existence and multiplicity of solutions.

scholarly journals A Variational Approach to Perturbed Discrete Anisotropic Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Amjad Salari ◽  
Giuseppe Caristi ◽  
David Barilla ◽  
Alfio Puglisi
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Results ◽  
Anisotropic Equation

We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

scholarly journals Existence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Chunyan He ◽  
Yongzhi Liao ◽  
Yongkun Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We investigate the existence and multiplicity of solutions to a boundary value problem for impulsive differential equations. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, at least two solutions, and infinitely many solutions. Some examples are given to illustrate the effectiveness of our results.

scholarly journals Multiplicity of solutions for the discrete boundary value problem involving the p-Laplacian

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdelrachid El Amrouss ◽  
Omar Hammouti
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Design Methodology ◽  
Boundary Value ◽  
Point Theory ◽  
Content Type ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

PurposeThe purpose of this paper is the study of existence and multiplicity of solutions for a nonlinear discrete boundary value problems involving the p-laplacian.Design/methodology/approachThe approach is based on variational methods and critical point theory.FindingsTheorem 1.1. Theorem 1.2. Theorem 1.3. Theorem 1.4.Originality/valueThe paper is original and the authors think the results are new.

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