Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 162, pp. 1-23.
Title: Existence of solutions to indefinite quasilinear
elliptic problems of p-q-Laplacian type
Author: Nikolaos E. Sidiropoulos (Technical Univ. of Crete, Greece)
Abstract:
We study the indefinite quasilinear elliptic problem
$$\displaylines{
-\Delta u-\Delta _{p}u=a(x)|u|^{q-2}u-b(x)|u|^{s-2}u
\quad\hbox{in }\Omega , \cr
u=0\quad\hbox{on }\partial \Omega ,
}$$
where $\Omega $ is a bounded domain in
$\mathbb{R}^{N}$, $N\geq 2$, with a sufficiently smooth boundary,
$q,s$ are subcritical exponents, $a(\cdot)$ changes
sign and $b(x)\geq 0$ a.e. in $\Omega$. Our proofs are variational
in character and are based either on the fibering method or the
mountain pass theorem.
Submitted July 7, 2010. Published November 12, 2010.
Math Subject Classifications: 35J60, 35J62, 35J92.
Key Words: Indefinite quasilinear elliptic problems;
subcritical nonlinearities; p-Laplacian;
p-q-Laplacian; fibering method; mountain pass theorem.