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.

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 Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1207
Author(s):  
Feng Xiong ◽  
Zhan Zhou
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Laplacian Operator

In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example.

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.

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.

TWO POSITIVE SOLUTIONS OF SOME SINGULAR BOUNDARY VALUE PROBLEMS

2010 ◽  
Vol 08 (03) ◽  
pp. 305-314 ◽  
Author(s):  
RADU PRECUP
Keyword(s):  
Boundary Value Problems ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problems

The existence of two positive solutions for a class of singular boundary value problems is established by means of a combination of the Leray–Schauder principle with techniques from critical point theory.

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