Existence of the positive solutions for a class of nonlinear elasticity problems involving Orlicz spaces via sub-supersolution method

Abstract

In this paper, we study nonlinear elastic problem of the type{−ΔΦu+K(x)u−α|u|LΛγ=λup|u|LΨq,inΩ,u=0,on∂Ω, where q,γ are positive constants and p,α∈(0,1). |⋅|LΨ, |⋅|LΛ and Φ are defined later. Based on the pseudomonotone operators theory, we establish some new sub-supersolution theorems, that generalize the results in [12]. In addition, based on the obtained theorems, we prove the existence of positive solutions to the above mentioned under certain assumptions about the parameters. Our work improves the results of some past researches.