Abstract:
The goal of this paper is to prove the existence of two weak
solutions for the following problem:
− div(|∇u|p(x)−2∇u+μ(x)|∇u|q(x)−2∇u)
=λh(x)u
−η(x)+ξ(x)|u|s(x)−2u in Ω,
u = 0 on ∂Ω,
where Ω ⊂ RN, N ≥ 2 is a bounded domain with smooth boundary
∂Ω and λ > 0 is a real parameter. The functions h(x), ξ(x) ∈ C(Ω) are
positive with compact support in Ω.We assume some suitable conditions
on functions p, q, η and s. We use the Nehari manifold method based on
fibering maps to establish our results.
Mathematics Subject Classification. 35J30, 35J75, 35D30.
Keywords. Nehari manifold,Musielak–Sobolev spaces, fibering map, double
phase operator with variable exponents