Existence Results for Singular p(x)-Laplacian Equation

Abstract

This paper is concerned with the existence of solutions for the following class of singular fourth order elliptic equations { Δ ( |x|p(x)|Δu|p(x)−2Δu ) = a(x)u−γ(x) + λf(x, u), in Ω, u = Δu = 0, on ∂Ω. where Ω is a smooth bounded domain in R , γ : Ω → (0, 1) be a continuous function, f ∈ C(Ω × R), p : Ω −→ (1,∞) and a is a function that is almost everywhere positive in Ω . Using variational techniques combined with the theory of the generalized Lebesgue-Sobolev spaces, we prove the existence at least one nontrivial weak solution. 2020 Mathematics Subject Classification. 46E35,26A45,28A12.