Existence of solutions for non-uniformly nonlinear elliptic systems

Abstract

Using a variational approach, we prove the existence of solutions for the degenerate quasilinear elliptic system $$displaylines{ -hbox{div}(u_1 (x)|abla u|^{p-2} abla u) =lambda F_u(x,u,v)+mu G_u(x,u,v),cr -hbox{div}(u_2 (x)|abla v|^{q-2} abla v) =lambda F_v(x,u,v)+mu G_v(x,u,v), }$$ with Dirichlet boundary conditions.

Keywords

• Non-uniformly elliptic system
• mountain pass theorem
• minimum principle