### 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.

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.

#### Keywords

Dirichlet problem; Radon measures; critical point theory

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