Geodesic
Existence of positive solutions for two nonlinear eigenvalue problems
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 31A25, 31A35, 34B15, 34B27, 35J65
Keywords: eigenvalue, kato class, Green's function, superharmonic function, shauder fixed point theorem, maximum principle 
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     author = {Rhouma, Nedra Belhaj and M\^aatoug, Lamia},
     title = {Existence of positive solutions for two nonlinear eigenvalue problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a39/}
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Rhouma, Nedra Belhaj; Mâatoug, Lamia. Existence of positive solutions for two nonlinear eigenvalue problems. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a39/