Multiplicity Results for a Class of Asymptotically Linear Elliptic Problems With Resonance and Applications to Problems With Measure Data

We study existence and multiplicity results for solutions of elliptic problems of the type -Delta u = g(x, u) in a bounded domain Omega with Dirichlet boundary conditions. The function g(x, s) is asymptotically linear as vertical bar s vertical bar -> +infinity. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type -Delta u = g(epsilon)(x, u) where g(epsilon)(x, s) -> g(x, s) as epsilon -> 0. The previous results find an application in the study of Dirichlet problems of the type -Delta u = g(x, u) + mu where mu is a Radon measure. To properly set the above mentioned problems in a variational framework we also study existence and properties of critical points of a class of abstract nonsmooth functional defined on Banach spaces and extend to this nonsmooth framework some classical linking theorems.