Existence and multiplicity results for semilinear equations with measure data

Abstract

In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation $-\Delta u=g(x,u)+\mu$ where $\mu$ is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity $g(x,u)$ and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments from critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.