scholarly journals A variational approach for fractional boundary value systems depending on two parameters

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 517-530
Author(s):  
Ghasem Afrouzi ◽  
Samad Kolagar ◽  
Armin Hadjian ◽  
Jiafa Xu
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Infinitely Many Solutions ◽  
Two Parameters

In this paper, we prove the existence of infinitely many solutions to nonlinear fractional boundary value systems, depending on two real parameters. The approach is based on critical point theory and variational methods. We also give an example to illustrate the obtained results.

scholarly journals Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 475 ◽  
Author(s):  
Fares Kamache ◽  
Rafik Guefaifia ◽  
Salah Boulaaras ◽  
Asma Alharbi
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Existence Of Weak Solutions ◽  
New Class ◽  
Two Parameters

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

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 Infinitely many solutions for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions

2019 ◽  
Vol 38 (4) ◽  
pp. 71-96 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Anderson Luis Albuquerque de Araujo ◽  
Amjad Salari
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variable Exponent ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Nonlocal Problems ◽  
Multiplicity Results

In this article we will provide new multiplicity results of the solutions for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions. We investigate the existence of infinitely many solutions for perturbed nonlocal problems with variable exponent and nonhomogeneous Neumann conditions. The approach is based on variational methods and critical point theory.

scholarly journals Nontrivial Solutions for Dirichlet Boundary Value Systems with the(p1,…,pn)-Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shang-Kun Wang ◽  
Wen-Wu Pan
Keyword(s):  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Nontrivial Solutions

Using critical point theory due to Bonanno (2012), we prove the existence of at least one nontrivial solution for Dirichlet boundary value systems with the(p1,…,pn)-Laplacian.

Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces

2018 ◽  
Vol 68 (4) ◽  
pp. 867-880
Author(s):  
Saeid Shokooh ◽  
Ghasem A. Afrouzi ◽  
John R. Graef
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Neumann Problems

Abstract By using variational methods and critical point theory in an appropriate Orlicz-Sobolev setting, the authors establish the existence of infinitely many non-negative weak solutions to a non-homogeneous Neumann problem. They also provide some particular cases and an example to illustrate the main results in this paper.

scholarly journals Infinitely many solutions for a nonlocal elliptic system of $(p_1,\ldots,p_n)$-Kirchhoff type with critical exponent

2021 ◽  
Vol 39 (5) ◽  
pp. 199-221
Author(s):  
Ghasem A. Afrouzi ◽  
Giuseppe Caristi ◽  
Amjad Salari
Keyword(s):  
Variational Methods ◽  
Critical Exponent ◽  
Critical Point ◽  
Elliptic System ◽  
Critical Point Theory ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Nontrivial Solutions ◽  
Kirchhoff Type

The existence of infinitely many nontrivial solutions for a nonlocal elliptic system of $(p_1,\ldots,p_n)$-Kirchhoff type with critical exponent is investigated. 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 Boundary value problems of a discrete generalized beam equation via variational methods

2018 ◽  
Vol 16 (1) ◽  
pp. 1412-1422
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi
Keyword(s):  
Variational Methods ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Beam Equation

AbstractThe authors explore the boundary value problems of a discrete generalized beam equation. Using the critical point theory, some sufficient conditions for the existence of the solutions are obtained. Several consequences of the main results are also presented. Examples are given to illustrate the theorems.

scholarly journals Multiple positive solutions for periodic boundary value problem via variational methods

2008 ◽  
Vol 39 (2) ◽  
pp. 111-120 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Periodic Boundary Value Problem ◽  
Multiple Positive Solutions

In this paper, we investigate the positive solutions of periodic boundary value problem. By using critical point theory the existence of multiple positive solutions is obtained.

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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