scholarly journals Multiple Solutions for the Discretep-Laplacian Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yuhua Long ◽  
Haiping Shi
Keyword(s):  
Boundary Value Problems ◽  
Critical Point ◽  
Point Theorem ◽  
Difference Equations ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Nonlinear Difference Equations ◽  
Critical Point Theorem

By employing a critical point theorem, established by Bonanno, we prove the existence of three distinct solutions to boundary value problems of nonlinear difference equations with a discretep-Laplacian operator. To demonstrate the applicability of our results, we also present an example.

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.

Difference equations in abstract spaces

1998 ◽  
Vol 64 (2) ◽  
pp. 277-284 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Difference Equations ◽  
Boundary Value ◽  
Existence Results ◽  
Second Order ◽  
Abstract Spaces

AbstractExistence results are presented for second order discrete boundary value problems in abstract spaces. Our analysis uses only Sadovskii's fixed point theorem.

Existence of three solutions for a three-point boundary value problem via a three-critical-point theorem

2015 ◽  
Vol 31 (2) ◽  
pp. 213-220
Author(s):  
XIAOJIE LIN ◽  
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Point Theorem ◽  
Reflexive Banach Space ◽  
Boundary Value ◽  
Main Tool ◽  
Multiplicity Result ◽  
Point Boundary ◽  
Three Solutions ◽  
Critical Point Theorem

In this paper, we study the existence of at least three solutions for a three-point boundary value problem. By constructing and showing an appropriate separable and reflexive Banach space, a new multiplicity result of the three-point boundary value problem is established. Our main tool is based upon variational method and three-critical-point theorem.

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