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 - δu = g(x,u) in a bounded domain ω with Dirichlet boundary conditions. The function g(x,s) is asymptotically linear as |s|→ +∞. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type - δu = g _∈(x,u) where g_∈(x,s) → g(x,s) as ∈→ 0. The previous results find an application in the study of Dirichlet problems of the type - δu = g(x, u) + μ where μ 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.