Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 42, pp. 1-10.

Title: A discontinuous problem involving the p-Laplacian operator
      and critical exponent in $\mathbb{R}^N$

Authors: Claudianor Oliveira Alves (Univ. Federal de Campina Grande, Brazil)
         Ana Maria Bertone (Univ. Federal da Paraiba, Brazil)

Abstract: 
 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.
 
Submitted September 23, 2002. Published April 16, 2003.
Math Subject Classifications: 35A15, 35J60, 35H30.
Key Words: Variational methods; discontinuous
           nonlinearities; critical exponents.