EXISTENCE RESULTS FOR FRACTIONAL BOUNDARY VALUE PROBLEM VIA CRITICAL POINT THEORY

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.

Download Full-text

Existence of Solutions for a Fourth-Order Boundary Value Problem with Nonlinear Derivative Dependence on the Half-Line via Critical Point Theory

Mediterranean Journal of Mathematics ◽

10.1007/s00009-019-1414-y ◽

2019 ◽

Vol 16 (6) ◽

Author(s):

Sihem Boumaraf ◽

Toufik Moussaoui

Keyword(s):

Boundary Value Problem ◽

Critical Point ◽

Fourth Order ◽

Critical Point Theory ◽

Existence Of Solutions ◽

Boundary Value ◽

Point Theory ◽

Half Line

Download Full-text

Existence of solutions for nonlinear fractional order p-Laplacian differential equations via critical point theory

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2019-0051 ◽

2019 ◽

Vol 22 (4) ◽

pp. 945-967

Author(s):

Nemat Nyamoradi ◽

Stepan Tersian

Keyword(s):

Differential Equations ◽

Variational Method ◽

Boundary Value Problem ◽

Critical Point ◽

Fractional Order ◽

Critical Point Theory ◽

Existence Of Solutions ◽

Point Theory ◽

Fractional Boundary Value Problem ◽

New Criteria

Abstract In this paper, we study the existence of solutions for a class of p-Laplacian fractional boundary value problem. We give some new criteria for the existence of solutions of considered problem. Critical point theory and variational method are applied.

Download Full-text

Solvability of fractional boundary value problem with p-Laplacian via critical point theory

Boundary Value Problems ◽

10.1186/s13661-016-0583-x ◽

2016 ◽

Vol 2016 (1) ◽

Cited By ~ 6

Author(s):

Taiyong Chen ◽

Wenbin Liu

Keyword(s):

Boundary Value Problem ◽

Critical Point ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Fractional Boundary Value Problem

Download Full-text

Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory

Abstract and Applied Analysis ◽

10.1155/2012/648635 ◽

2012 ◽

Vol 2012 ◽

pp. 1-21 ◽

Cited By ~ 15

Author(s):

Jing Chen ◽

X. H. Tang

Keyword(s):

Boundary Value Problem ◽

Critical Point ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Fractional Boundary Value Problem ◽

Multiplicity Of Solutions ◽

Existence And Multiplicity

Download Full-text

Existence of solutions for a fourth-order boundary value problem on the half-line via critical point theory

Electronic journal of qualitative theory of differential equations ◽

10.14232/ejqtde.2016.1.24 ◽

2016 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Mabrouk Briki ◽

Toufik Moussaoui ◽

Donal O'Regan

Keyword(s):

Boundary Value Problem ◽

Critical Point ◽

Fourth Order ◽

Critical Point Theory ◽

Existence Of Solutions ◽

Boundary Value ◽

Point Theory ◽

Half Line

Download Full-text

Existence of Solutions for a Class of Fractional Boundary Value Equations with Impulsive Effects via Critical Point Theory

Mediterranean Journal of Mathematics ◽

10.1007/s00009-018-1122-z ◽

2018 ◽

Vol 15 (3) ◽

Cited By ~ 5

Author(s):

Nemat Nyamoradi ◽

Elham Tayyebi

Keyword(s):

Critical Point ◽

Critical Point Theory ◽

Existence Of Solutions ◽

Boundary Value ◽

Point Theory ◽

Impulsive Effects

Download Full-text

Solvability of Boundary Value Problems for Impulsive Fractional Differential Equations Via Critical Point Theory

Mediterranean Journal of Mathematics ◽

10.1007/s00009-016-0779-4 ◽

2016 ◽

Vol 13 (6) ◽

pp. 4845-4866 ◽

Cited By ~ 5

Author(s):

Yanning Wang ◽

Yongkun Li ◽

Jianwen Zhou

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Critical Point ◽

Fractional Differential Equations ◽

Critical Point Theory ◽

Boundary Value ◽

Point Theory ◽

Impulsive Fractional Differential Equations ◽

Fractional Differential

Download Full-text

Existence and multiple solutions for a second-order difference boundary value problem via critical point theory

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.03.017 ◽

2007 ◽

Vol 326 (1) ◽

pp. 511-520 ◽

Cited By ~ 54

Author(s):

Haihua Liang ◽

Peixuan Weng

Keyword(s):

Boundary Value Problem ◽

Critical Point ◽

Critical Point Theory ◽

Multiple Solutions ◽

Boundary Value ◽

Point Theory ◽

Second Order ◽

Order Difference

Download Full-text

A Variational Approach to Perturbed Discrete Anisotropic Equations

Abstract and Applied Analysis ◽

10.1155/2016/5676138 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 1

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.

Download Full-text

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.281.312 ◽

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.

Download Full-text