scholarly journals Three Solutions for Inequalities Dirichlet Problem Driven byp(x)-Laplacian-Like

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhou Qing-Mei ◽  
Ge Bin
Keyword(s):  
Dirichlet Problem ◽  
Critical Point ◽  
Point Theorem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Critical Point Theorem ◽  
Nonlinear Elliptic ◽  
Locally Lipschitz

A class of nonlinear elliptic problems driven byp(x)-Laplacian-like with a nonsmooth locally Lipschitz potential was considered. Applying the version of a nonsmooth three-critical-point theorem, existence of three solutions of the problem is proved.

scholarly journals Existence results for nonlinear elliptic problems on fractal domains

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Massimiliano Ferrara ◽  
Giovanni Molica Bisci ◽  
Dušan Repovš
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Critical Point ◽  
Elliptic Problems ◽  
Open Interval ◽  
Existence Results ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Fractal Domains ◽  
Critical Point Result

AbstractSome existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution.

Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Qing-Mei Zhou ◽  
Ke-Qi Wang
Keyword(s):  
Eigenvalue Problem ◽  
Critical Points ◽  
Fractional Laplacian ◽  
Nonlinear Eigenvalue Problem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractIn this paper we consider a nonlinear eigenvalue problem driven by the fractional Laplacian. By applying a version of the three-critical-points theorem we obtain the existence of three solutions of the problem in

Existence of three solutions for a three-point boundary value problem via a three-critical-point theorem

2015 ◽  
Vol 31 (2) ◽  
pp. 213-220
Author(s):  
XIAOJIE LIN ◽  
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Point Theorem ◽  
Reflexive Banach Space ◽  
Boundary Value ◽  
Main Tool ◽  
Multiplicity Result ◽  
Point Boundary ◽  
Three Solutions ◽  
Critical Point Theorem

In this paper, we study the existence of at least three solutions for a three-point boundary value problem. By constructing and showing an appropriate separable and reflexive Banach space, a new multiplicity result of the three-point boundary value problem is established. Our main tool is based upon variational method and three-critical-point theorem.

On the existence of eigenvalues for some nonlinear elliptic and hyperbolic problems

1985 ◽  
Vol 101 (3-4) ◽  
pp. 297-305
Author(s):  
Nicola Basile ◽  
Michele Mininni
Keyword(s):  
Critical Point ◽  
Point Theorem ◽  
Selfadjoint Operator ◽  
Eigenvalue Problems ◽  
Hyperbolic Equations ◽  
Main Tool ◽  
Hyperbolic Problems ◽  
Critical Point Theorem ◽  
Nonlinear Elliptic

SynopsisIn this paper some eigenvalue problems for elliptic as well as hyperbolic equations are solved. The main tool used is an abstract critical point theorem on an unbounded manifold of the form {u | (Lu, u) = constant} (where L is a nonpositive selfadjoint operator), which makes use of a linking type argument on a manifold.

scholarly journals Three solutions to discrete anisotropic problems with two parameters

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Marek Galewski ◽  
Piotr Kowalski
Keyword(s):  
Critical Point ◽  
Point Theorem ◽  
Three Solutions ◽  
Critical Point Theorem ◽  
Multiplicity Of Solutions ◽  
Anisotropic Problems ◽  
Two Parameters

AbstractIn this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.

Infinitely Many Solutions for Mixed Elliptic Problems Involving the p−Laplacian

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Gabriele Bonanno ◽  
Giuseppina D’Aguí ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Boundary Conditions ◽  
Critical Point ◽  
Critical Point Theory ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Point Theory ◽  
Laplacian Operator ◽  
Infinitely Many Solutions ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

AbstractIn this paper the existence of infinitely many solutions for nonlinear elliptic problems involving the p-Laplacian operator with mixed Dirichlet-Neumann boundary conditions is established. The key assumption is a suitable oscillating behavior, either at infinity or at zero, of the nonlinearity. The approach is based on the critical point theory.

Sign in / Sign up

Export Citation Format

Share Document