scholarly journals Multiplicity of solutions for variable exponent Dirichlet problem with concave term

2012 ◽  
Vol 5 (4) ◽  
pp. 845-855 ◽  
Author(s):  
V. V. Motreanu ◽  
Keyword(s):  
Dirichlet Problem ◽  
Variable Exponent ◽  
Multiplicity Of Solutions ◽  
Concave Term

scholarly journals Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-36 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Smooth Solutions ◽  
Dirichlet Problems ◽  
Unbounded Potential ◽  
Indefinite Potential ◽  
Truncation Techniques ◽  
Concave Term

We consider a parametric semilinear Dirichlet problem with an unbounded and indefinite potential. In the reaction we have the competing effects of a sublinear (concave) term and of a superlinear (convex) term. Using variational methods coupled with suitable truncation techniques, we prove two multiplicity theorems for small values of the parameter. Both theorems produce five nontrivial smooth solutions, and in the second theorem we provide precise sign information for all the solutions.

scholarly journals Multiple Solutions for the p(x)− Laplace Operator with Critical Growth

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Analia Silva
Keyword(s):  
Elliptic Equation ◽  
Laplace Operator ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equation ◽  
Critical Growth ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δ

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