# American Institute of Mathematical Sciences

September  2006, 5(3): 571-581. doi: 10.3934/cpaa.2006.5.571

## Positive radial solutions for some quasilinear elliptic systems in exterior domains

 1 Departamento de Matemática, Universidade Fededral da Paraíba, 58059-900, João Pessoa-PB, Brazil 2 Departamento de Matemática, Universidad de Tarapacá, Casilla 7-D, Arica, Chile 3 Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile 4 Departamento de Matemáticas y C. C.,Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

Received  November 2004 Revised  November 2005 Published  June 2006

We use fixed-point theorem of cone expansion/compression type to prove the existence of positive radial solutions for the following class of quasilinear elliptic systems in exterior domains

$-\Delta_p u = k_1(|x| )f(u,v),$ for $|x| > 1$ and $x \in \mathbb R^N,$

$-\Delta_p v = k_2(|x|)g(u,v),$ for $|x| > 1$ and $x \in \mathbb R^N,$

$u(x) = v(x) =0,$ for $|x| =1,$

$u(x), v(x) \rightarrow 0$ as $|x| \rightarrow +\infty,$

where $1 < p < N$ and $\Delta_p u=$ div $(|\nabla u|^{p-2}\nabla u )$ is the p-Laplacian operator. We consider nonlinearities that are either superlinear or sublinear.

Citation: João Marcos do Ó, Sebastián Lorca, Justino Sánchez, Pedro Ubilla. Positive radial solutions for some quasilinear elliptic systems in exterior domains. Communications on Pure & Applied Analysis, 2006, 5 (3) : 571-581. doi: 10.3934/cpaa.2006.5.571
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