Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition

R. A. Mashiyev, B. Cekic, M. Avci, Z. Yucedag

Research output: Contribution to journalJournal Articlepeer-review

37 Citations (Scopus)

Abstract

We discuss the problem - div(a(x, ∇u)) = m(x){divides}u{divides}r(x)-2u + n(x){divides}u{divides}s(x)-2u in Ω, where Ω is a bounded domain with smooth boundary in ℝN(N ≥ 2), and div(a(x, ∇u)) is a p(x)-Laplace type operator with 1 & r(x) & p(x) & s(x). We show the existence of infinitely many nontrivial weak solutions in. Our approach relies on the theory of the variable exponent Lebesgue and Sobolev spaces combined with adequate variational methods and a variation of the Mountain Pass lemma and critical point theory.

Original languageEnglish
Article number598928
Pages (from-to)579-595
Number of pages17
JournalComplex Variables and Elliptic Equations
Volume57
Issue number5
DOIs
Publication statusPublished - May 2012

Keywords

  • critical point
  • Ekeland's variational principle
  • Mountain Pass theorem
  • multiple solutions
  • nonuniform elliptic equations
  • p(x)-Laplace operator

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