Geodesic
Existence of solutions to nonlocal elliptic equations with discontinuous terms
Electronic Journal of Differential Equations, Tome 2012 (2012).

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

Summary: In this article, we study the existence of nonnegative solutions for the elliptic partial differential equation $$\displaylines{ -[M(\|u\|^{p}_{1,p})]^{1,p}\Delta_{p}u = f(x,u) \quad\hbox{in } \Omega , \cr u = 0 \quad\hbox{on } \partial\Omega , }$$ where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain, $f:\overline{\Omega}\times \mathbb{R}^+\to \mathbb{R}$ is a discontinuous nonlinear function.
Classification : 35A15, 35J40, 34A36
Keywords: variational methods, elliptic problem, discontinuous nonlinearity 
@article{EJDE_2012__2012__a16,
     author = {Correa, Francisco Julio S.A. and Nascimento, Rubia G.},
     title = {Existence of solutions to nonlocal elliptic equations with discontinuous terms},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a16/}
}
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Correa, Francisco Julio S.A.; Nascimento, Rubia G. Existence of solutions to nonlocal elliptic equations with discontinuous terms. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a16/