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.

Show me the PDF file (221 KB), TEX file, and other files for this article.

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

Return to the EJDE web page