## Topological Methods in Nonlinear Analysis

### 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.

#### Article information

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

Dates
First available in Project Euclid: 13 May 2016

https://projecteuclid.org/euclid.tmna/1463144819

Mathematical Reviews number (MathSciNet)
MR2289689

Zentralblatt MATH identifier
1136.35044

#### Citation

Ferrero, Alberto; Saccon, Claudio. Existence and multiplicity results for semilinear equations with measure data. Topol. Methods Nonlinear Anal. 28 (2006), no. 2, 285--318. https://projecteuclid.org/euclid.tmna/1463144819

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