Existence and multiplicity of solutions for a class of quasilinear elliptic equations: An Orlicz–Sobolev space setting

AbstractIn this paper, we study the existence and multiplicity of solutions of the following quasilinear elliptic problem{−div(a(|∇u|)∇u)=f(x,u),in Ω,u=0,on ∂Ω, where Ω⊂RN is a bounded domain with smooth boundary ∂Ω. The existence and multiplicity of solutions are obtained by genus theory, symmetric mountain pass lemma, fountain theorem and dual fountain theorem, respectively