Entropy solutions for some elliptic problems involving the generalized p(u)-Laplacian operator

Infinitely Many Solutions for a Steklov Problem Involving the p(x)-Laplacian Operator

By using variational methods and critical point theory for smooth functionals defined on a reflexive Banach space, we establish the existence of infinitely many weak solutions for a Steklov problem involving the p(x)-Laplacian depending on two parameters. We also give some corollaries and applicable examples to illustrate the obtained result../files/site1/files/42/4Abstract.pdf

MULTIPLE NONNEGATIVE SOLUTIONS FOR ELLIPTIC BOUNDARY VALUE PROBLEMS INVOLVING THE p -LAPLACIAN

In this paper we present a result concerning the existence of two nonzero nonnegative solutions for the following Dirichlet problem involving the p -Laplacian ( −∆pu = λf(x, u) in Ω, u = 0 on ∂Ω, using variational methods. In particular, we will determine an explicit real interval Λ for which these solutions exist for every λ ∈ Λ. We also point out that our result improves and extends to higher...

Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator

The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.

Existence of positive solutions to elliptic problems involving the fractional Laplacian

Multiple solutions to a class of inclusion problems with operator involving p ( x ) - Laplacian

In this paper, we prove the existence of at least two nontrivial solutions for a nonlinear elliptic problem involving p(x)-Laplacian-like operator and nonsmooth potentials. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.