scholarly journals Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zuoshi Xie ◽  
Yuanfeng Jin ◽  
Chengmin Hou
Keyword(s):  
Boundary Value Problem ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Multiple Solutions ◽  
Mountain Pass Theorem ◽  
Boundary Value ◽  
Point Theory ◽  
Linking Theorem ◽  
Fractional Difference ◽  
Variational Framework

By establishing the corresponding variational framework and using the mountain pass theorem, linking theorem, and Clark theorem in critical point theory, we give the existence of multiple solutions for a fractional difference boundary value problem with parameter. Under some suitable assumptions, we obtain some results which ensure the existence of a well precise interval of parameter for which the problem admits multiple solutions. Some examples are presented to illustrate the main results.

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.

EXISTENCE RESULTS FOR FRACTIONAL BOUNDARY VALUE PROBLEM VIA CRITICAL POINT THEORY

2012 ◽  
Vol 22 (04) ◽  
pp. 1250086 ◽  
Author(s):  
FENG JIAO ◽  
YONG ZHOU
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Critical Point Theory ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Theory ◽  
Fractional Boundary Value Problem ◽  
Fractional Differential ◽  
Left And Right ◽  
First Time

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.

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

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.

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.

scholarly journals Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Wang ◽  
Yansheng Liu ◽  
Yujun Cui
Keyword(s):  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Point Theory ◽  
Fractional Boundary Value Problem ◽  
Fountain Theorems ◽  
Left And Right ◽  
Variant Fountain Theorems ◽  
Derivatives Of

This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux,  x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess  infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.

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.

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