Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 167, pp. 1-9.
Title: Existence of solutions for non-uniformly nonlinear elliptic systems
Authors: Ghasem Alizadeh Afrouzi (Univ. of Mazandaran, Babolsar, Iran)
Somayeh Mahdavi (Univ. of Mazandaran, Babolsar, Iran)
Nikolaos B. Zographopoulos (Univ. of Military Education, Athens, Greece)
Abstract:
Using a variational approach, we prove the existence of
solutions for the degenerate quasilinear elliptic system
$$\displaylines{
-\hbox{div}(\nu_1 (x)|\nabla u|^{p-2} \nabla u)
=\lambda F_u(x,u,v)+\mu G_u(x,u,v),\cr
-\hbox{div}(\nu_2 (x)|\nabla v|^{q-2} \nabla v)
=\lambda F_v(x,u,v)+\mu G_v(x,u,v),
}$$
with Dirichlet boundary conditions.
Submitted November 12, 2011. Published December 14, 2011.
Math Subject Classifications: 34B18, 35B40, 35J65.
Key Words: Non-uniformly elliptic system; mountain pass theorem;
minimum principle.