Multiplicity of weak solutions for a class of nonuniformly elliptic equations of p -Laplacian type

This paper deals with the multiplicity of weak solutions in W01(Ω) to a class of nonuniformly elliptic equations of the form −div(a(x,∇u))=h(x)|u|r−1u+g(x)|u|s−1u in a bounded domain ΩΩ of RNRN. Here aa satisfies |a(x,ξ)|≦c0(h0(x)+h1(x)|ξ|p−1)|a(x,ξ)|≦c0(h0(x)+h1(x)|ξ|p−1) for all ξ∈RNξ∈RN, a.e. x∈Ωx∈Ω, h0∈Lpp−1(Ω), h1∈Lloc1(Ω), h1(x)≧1h1(x)≧1 for a.e. xx in ΩΩ, 1