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 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 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 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 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.

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.

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