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.