Existence and multiplicity of solutions for a class of quasilinear problems in Orlicz-Sobolev spaces

2016/04/04 by Ait-Mahiout, Karima, Alves, Claudianor O.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.00808

Abstract

This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems -Δ_Φu+ϕ(|u|)u=f(u)~in ~Ω_λ, u(x)gt;0 ~in~Ω_λ, u=0~ on ~∂Ω_λ, where Φ(t)=∫₀^|t| ϕ(s) s ds is an N-function, Δ_Φ is the Φ-Laplacian operator, \linebreak Ω_λ=λΩ, Ω is a smooth bounded domain in ℝ^N, N ≥ 2, λ is a positive parameter and f: ℝ→ ℝ is a continuous function. Here, we use variational methods to get multiplicity of solutions by using of Lusternik-Schnirelmann category of Ω in itself.

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