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)

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November 25, 2004

 

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