Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 177, pp. 1-9.

Title: Existence of positive solutions for p(x)-Laplacian problems

Authors: Ghasem A. Afrouzi (Mazandaran Univ., Babolsar, Iran)
         Horieh Ghorbani   (Mazandaran Univ., Babolsar, Iran)

Abstract: 
 We consider the system of differential equations
 $$\displaylines{
  -\Delta_{p(x)} u=\lambda [g(x)a(u) + f(v)] \quad\hbox{in }\Omega\cr
  -\Delta_{q(x)} v=\lambda [g(x)b(v) + h(u)] \quad\hbox{in }\Omega\cr
   u=v= 0 \quad\hox{on } \partial \Omega
 }$$
 where $p(x) \in C^1(\mathbb{R}^N)$ is a radial symmetric function
 such that  $\sup|\nabla p(x)| < \infty$,
 $1 < \inf p(x) \leq \sup p(x) < \infty$, and where
 $-\Delta_{p(x)} u = -{\rm div}|\nabla u|^{p(x)-2}\nabla u$
 which is called the $p(x)$-Laplacian.
 We discuss the existence of positive solution via
 sub-super-solutions without assuming  sign conditions on
 $f(0),h(0)$.
 
Submitted July 18, 2007. Published December 17, 2007.
Math Subject Classifications: 35J60, 35B30, 35B40
Key Words: Positive radial solutions; p(x)-Laplacian problems;
           boundary value problems.