Nontrivial solutions of some quasilinear problems via a cohomological local splitting

This paper deals with a generalization of the pp-Laplacian type boundary value problem {−div(pĀ(x,u)|∇u|p−2∇u)+Āt(x,u)|∇u|p=g(x,u)in Ω,u=0on ∂Ω,ΩΩ being a bounded domain in RNRN.Under suitable assumptions and if p>Np>N, the existence of a nontrivial solution can be proved by means of variational tools and a cohomological local splitting.