## Relatório de pesquisa 49/04

Francisco O. V. De Paiva and Eugenio Massa, Multiple Solutions for Some Elliptic Equations With a Nonlinearity Concave in the Origin

Abstract
In this paper we establish the existence of multiple solutions for the semilinear elliptic problem
$\begin{array}{lll} -\Delta u = -\lambda |u|^{q-2}u +au+g(u) & {\rm in} & \Omega\\ \ \ \ \ u = 0 & {\rm on} & \partial \Omega, \end{array}$
where $\Omega \subset \mathbb{R}^N$ is a bounded domain with smooth boundary  $\partial \Omega$, $g:\mathbb{R}\to \mathbb{R}$ is a function of class $C^1$ such that $g(0)=g'(0)=0$, $\lambda>0$ is real parameter, $a\in\R$, and $1<q<2$.  We study the problem when $g$ is superlinear, asymptotically linear and asymmetric or infinity.

Key words and phrases:  multiplicity of solution

1991 Mathematical Subject Classification: 35J65 (35J20)

If you are interested in obtaining a copy of this Report please contact the authors either via e-mail or by snail mail, at the address:
IMECC, UNICAMP
Cx. P. 6065
13083-970 Campinas, SP, BRAZIL

November 25, 2004

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