scholarly journals Infinitely many weak solutions for some elliptic problems in RN

2016 ◽  
Vol 100 (114) ◽  
pp. 271-278
Author(s):  
Mehdi Khodabakhshi ◽  
Abdolmohammad Aminpour ◽  
Mohamad Tavani
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Elliptic Problems ◽  
Point Theory

We investigate the existence of infinitely many weak solutions to some elliptic problems involving the p-Laplacian in RN by using variational method and critical point theory.

scholarly journals Weak Solutions for ap-Laplacian Antiperiodic Boundary Value Problem with Impulsive Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
Jiafa Xu ◽  
Wei Dong
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Point Theory ◽  
Existence Of Weak Solutions

By virtue of variational method and critical point theory, we will investigate the existence of weak solutions for ap-Laplacian impulsive differential equation with antiperiodic boundary conditions.

scholarly journals Twoweak solutions for a singular (p,q)-Laplacian problem

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3399-3407 ◽  
Author(s):  
F. Behboudi ◽  
A. Razani
Keyword(s):  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Laplacian Operator ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Smooth Bounded Domain

Here, a singular boundary value problem involving the (p,q)-Laplacian operator in a smooth bounded domain in RN is considered. Using the variational method and critical point theory, the existence of two weak solutions is proved.

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 Method for Multivalued Boundary Value Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Droh Arsène Béhi ◽  
Assohoun Adjé
Keyword(s):  
Variational Method ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Laplacian Operator ◽  
Differential Systems ◽  
Lagrange Functional ◽  
Special Case

In this paper, we investigate the existence of solution for differential systems involving a ϕ−Laplacian operator which incorporates as a special case the well-known p−Laplacian operator. In this purpose, we use a variational method which relies on Szulkin’s critical point theory. We obtain the existence of solution when the corresponding Euler–Lagrange functional is coercive.

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

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.

Impulsive differential inclusions via variational method

2017 ◽  
Vol 24 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Mouffak Benchohra ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Differential Inclusion ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Impulsive Differential Inclusions

AbstractIn this paper, we establish several results about the existence of second-order impulsive differential inclusion with periodic conditions. By using critical point theory, several new existence results are obtained. We also provide an example in order to illustrate the main abstract results of this paper.

scholarly journals Elliptic problems with nonmonotone discontinuities at resonance

2002 ◽  
Vol 7 (9) ◽  
pp. 497-507
Author(s):  
Halidias Nikolaos
Keyword(s):  
Critical Point ◽  
Existence Theorem ◽  
Critical Point Theory ◽  
Elliptic Problems ◽  
Point Theory ◽  
Forcing Term ◽  
At Resonance ◽  
Locally Lipschitz

Using the critical point theory of Chang (1981) for locally Lipschitz functionals, we prove an existence theorem for some elliptic problems at resonance with no Carathéodory forcing term.

scholarly journals Weak Solutions for ap-Laplacian Impulsive Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wei Dong ◽  
Jiafa Xu ◽  
Xiaoyan Zhang
Keyword(s):  
Differential Equation ◽  
Variational Method ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Impulsive Differential Equation ◽  
Dirichlet Boundary ◽  
Point Theory ◽  
Existence Results ◽  
Dirichlet Boundary Conditions

By the virtue of variational method and critical point theory, we give some existence results of weak solutions for ap-Laplacian impulsive differential equation with Dirichlet boundary conditions.

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.

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