Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 16, pp. 1-16.
Title: Existence of positive solutions for two nonlinear eigenvalue problems
Authors: Nedra Belhaj Rhouma (Inst. Prep. Etudes d'ingenieurs, Tunisia)
Lamia Maatoug (Faculte des Sciences de Tunis, Tunisia)
Abstract:
We study the existence of positive solutions for the following
two nonlinear eigenvalue problems
$$\displaylines{
\Delta u-g(.,u)u+\lambda f(.,u)u=0, \cr
\Delta u-g(.,u)u+\lambda f(.,u)=0,
}$$
in a bounded regular domain in $\mathbb{R}^{2}$
with $u=0$ on the boundary. We assume that $f$ and $g$ are
in Kato class of functions.
Submitted October 14, 2002. Published February 15, 2003.
Math Subject Classifications: 31A25, 31A35, 34B15, 34B27, 35J65
Key Words: Eigenvalue; Kato class; Green's function; superharmonic
function; Shauder fixed point theorem; maximum principle.