Electron. J. Diff. Equ., Vol. 2011 (2011), No. 167, pp. 1-9.

Existence of solutions for non-uniformly nonlinear elliptic systems

Ghasem Alizadeh Afrouzi, Somayeh Mahdavi, Nikolaos B. Zographopoulos

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.

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Ghasem Alizadeh Afrouzi
Department of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email: afrouzi@umz.ac.ir
Somayeh Mahdavi
Department of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email: smahdavi@umz.ac.ir
  Nikolaos B. Zographopoulos
University of Military Education, Hellenic Army Academy
Department of Mathematics & Engineering Sciences
Vari - 16673, Athens, Greece
email: nzograp@gmail.com, zographopoulosn@sse.gr

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