# Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity

@inproceedings{Figueiredo2006MultiplicityRF,
title={Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity},
author={Djairo Guedes de Figueiredo and J. P. Gossez and Pedro Ubilla},
year={2006}
}
In this paper we study the existence, nonexistence and multiplicity of positive solutions for the family of problems $-\Delta u = f_\lambda (x,u)$, $u \in H^1_0(\Omega)$, where $\Omega$ is a bounded domain in $\mathbb{R}^N$, $N\geq 3$ and $\lambda>0$ is a parameter. The results include the well-known nonlinearities of the Ambrosetti-Brezis-Cerami type in a more general form, namely $\lambda a (x)u^q + b(x) u^p$, where \$0 \leq q<1

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