Electron. J. Diff. Eqns., Vol. 2004(2004), No. 56, pp. 1-15.

Positive solutions for a class of quasilinear singular equations

Jose Valdo Goncalves & Carlos Alberto P. Santos

Abstract:
This article concerns the existence and uniqueness of solutions to the quasilinear equation
$$ -\Delta_p u=\rho(x) f(u) \quad \hbox{in } \mathbb{R}^N $$
with $u greater than 0$ and $u(x)\to 0$ as $|x| \to \infty$. Here $1 less than p less than \infty$, $N \geq 3$, $\Delta_{p}$ is the $p$-Laplacian operator, $\rho$ and $f$ are positive functions, and $f$ is singular at 0. Our approach uses fixed point arguments, the shooting method, and a lower-upper solutions argument.

Submitted October 6, 2003. Published April 13, 2004.
Math Subject Classifications: 35B40, 35J25, 35J60.
Key Words: Singular equations, radial positive solutions, fixed points, shooting method, lower-upper solutions

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Jose Valdo Goncalves
Universidade de Brasilia
Departamento de Matematica
70910-900 Brasilia, DF, Brasil
email: jv0ag@unb.br
Carlos Alberto P. Santos
Universidade Federal de Goias
Departamento de Matematica
Catalao, GO, Brasil
email: csantos@unb.br

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