Geodesic
Existence of positive solutions for two nonlinear eigenvalue problems
Electronic journal of differential equations, Tome 2003 (2003)
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 
@article{EJDE_2003__2003__a139,
     author = {Rhouma,  Nedra Belhaj and M\^aatoug,  Lamia},
     title = {Existence of positive solutions for two nonlinear eigenvalue problems},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1013.35059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a139/}
}
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AU  - Mâatoug,  Lamia
TI  - Existence of positive solutions for two nonlinear eigenvalue problems
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VL  - 2003
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%A Mâatoug,  Lamia
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%J Electronic journal of differential equations
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%F EJDE_2003__2003__a139
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__a139/