Geodesic
A discontinuous problem involving the \(p\)-Laplacian operator and critical exponent in \(\mathbb R^N\)
Electronic journal of differential equations, Tome 2003 (2003)
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 \(\mathbb {R^N\)}},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1109.35330},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a156/}
}
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AU  - Bertone,  Ana Maria
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%A Bertone,  Ana Maria
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%J Electronic journal of differential equations
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%F EJDE_2003__2003__a156
Alves,  Claudianor Oliveira; Bertone,  Ana Maria. A discontinuous problem involving the \(p\)-Laplacian operator and critical exponent in \(\mathbb R^N\). Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a156/