Topological Methods in Nonlinear Analysis

Existence and multiplicity results for semilinear equations with measure data

Alberto Ferrero and Claudio Saccon

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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.

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Topol. Methods Nonlinear Anal., Volume 28, Number 2 (2006), 285-318.

First available in Project Euclid: 13 May 2016

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Ferrero, Alberto; Saccon, Claudio. Existence and multiplicity results for semilinear equations with measure data. Topol. Methods Nonlinear Anal. 28 (2006), no. 2, 285--318.

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