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

Author(s):  
Tao Zhou ◽  
Xia Liu ◽  
Haiping Shi

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.

2013 ◽  
Vol 281 ◽  
pp. 312-318
Author(s):  
Fang Su ◽  
Xue Wen Qin

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.


2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Tieshan He ◽  
Fengjian Yang

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.


2012 ◽  
Vol 22 (04) ◽  
pp. 1250086 ◽  
Author(s):  
FENG JIAO ◽  
YONG ZHOU

In this paper, by the critical point theory, the boundary value problem is discussed for a fractional differential equation containing the left and right fractional derivative operators, and various criteria on the existence of solutions are obtained. To the authors' knowledge, this is the first time, the existence of solutions to the fractional boundary value problem is dealt with by using critical point theory.


2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhenguo Wang ◽  
Zhan Zhou

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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