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 |sj|\to +\infty. Also resonant situations are allowed. We also prove some perturbation results for Dirichlet problems of the type -Δu = g_\eps(x; u) where g_\eps(x,s)\to g(x,s) as \eps\to 0. The previous results find an application in the study of Dirichlet problems of the type -Δu = 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.