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On a class of nonhomogenous quasilinear problems in Orlicz-Sobolev spaces

Souayah A. K.

Opuscula Mathematica

2012

Vol. 32, no. 4

731-750

We study the nonlinear boundary value problem [formula], where Ω is a bounded domain in RN with smooth boundary, λ, μ are positive real numbers, q and α are continuous functions and a1,a2 are two mappings such that a1 (/t/)t; a2(/t/)t; are increasing homeomorphisms from R to R. The problem is analysed in the context of Orlicz-Soboev spaces. First we show the existence of infinitely many weak solutions for any λ, μ > 0. Second we prove that for any μ > 0, there exists λ* sufficiently small, and λ* large enough such that for any λ ∈ (0, λ*) ∪ (λ*, ∞), the above nonhomogeneous quasilinear problem has a non-trivial weak solution.