Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

Abstract

We study a non-homogeneous boundary value problem in a smooth bounded domain in ${\mathbb{R}}^N$. We prove the existence of at least two nonnegative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.

arXiv commentarXiv admin note: text overlap with arXiv:math/0607553

References in corpus (1)

• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

Cited by in corpus (3)

• Existence and regularity of positive solutions of quasilinear elliptic problems with singular semilinear term
• Existence of solutions for a quasilinear elliptic system with local nonlinearity on ${\mathbb{R}}^N$
• Multiplicity of solutions for a class of quasilinear equations involving critical Orlicz-Sobolev nonlinear term