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.