Existence and stability of solutions of general semilinear elliptic equations with measure data

Abstract

We study existence and stability for solutions of $Lu+g(x; u) = \omega$ in the closure of open set $\Omega$ where L is a second order elliptic operator, $g$ a Caratheodory function and $\omega$ a measure in $\bar\Omega$. We present a uni ed theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.