Multiple solutions for p-Laplacian type problems with asymptotically p-linear terms via a cohomological index theory

The aim of this paper is investigating the existence of weak solutions of the quasilinear elliptic model problem{−div(A(x,u)|∇u|p−2∇u)+1pAt(x,u)|∇u|p=f(x,u)in Ω,u=0on ∂Ω, where Ω⊂RNΩ⊂RN is a bounded domain, N≥2N≥2, p>1p>1, A   is a given function which admits partial derivative At(x,t)=∂A∂t(x,t) and f is asymptotically p-linear at infinity.Under suitable hypotheses both at the origin and at infinity, and if A(x,⋅)A(x,⋅) is even while f(x,⋅)f(x,⋅) is odd, by using variational tools, a cohomological index theory and a related pseudo-index argument, we prove a multiplicity result if p>Np>N in the non-resonant case.