Electron. J. Diff. Eqns., Vol. 2006(2006), No. 84, pp. 1-6.

Existence and uniqueness results of positive solutions for nonvariational quasilinear elliptic systems

Dimitrios A. Kandilakis, Nikolaos E. Sidiropoulos

Abstract:
We provide conditions for the existence and uniqueness of positive solutions to the quasilinear elliptic system
$$\displaylines{ -\Delta _{p}u=f(x,u,v) \cr -\Delta _{q}v=g(x,u,v) }$$
with Dirichlet boundary conditions on a bounded domain $\Omega \subseteq \mathbb{R}^N$.

Submitted April 6, 2006. Published July 27, 2006.
Math Subject Classifications: 35B50, 35D05, 35J55.
Key Words: Quasilinear elliptic system; nonvariational system; maximum principle; uniqueness; positive solution.

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Dimitrios A. Kandilakis
Department of Sciences
Technical University of Crete
73100 Chania, Greece
email: dkan@science.tuc.gr
Nikolaos E. Sidiropoulos
Department of Sciences
Technical University of Crete
73100 Chania, Greece
email: nsid@science.tuc.gr

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