Geodesic
A discontinuous problem involving the $p$-Laplacian operator and critical exponent in $\Bbb R^N$
Electronic Journal of Differential Equations, Tome 2003 (2003).

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

Summary: Using convex analysis, we establish the existence of at least two nonnegative solutions for the quasilinear problem $$ -\Delta_{p}u=H(u-a)u^{p^*-1} +\lambda h(x)\quad\hbox{in }\mathbb{R}^N $$ where $\Delta_{p}u$ is the $p$-Laplacian operator, $H$ is the Heaviside function, $p^*$ is the Sobolev critical exponent, and $h$ is a positive function.
Classification : 35A15, 35J60, 35H30
Keywords: variational methods, discontinuous nonlinearities, critical exponents 
@article{EJDE_2003__2003__a156,
     author = {Alves, Claudianor Oliveira and Bertone, Ana Maria},
     title = {A discontinuous problem involving the $p${-Laplacian} operator and critical exponent in $\Bbb R^N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a156/}
}
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Alves, Claudianor Oliveira; Bertone, Ana Maria. A discontinuous problem involving the $p$-Laplacian operator and critical exponent in $\Bbb R^N$. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a156/