Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 56, pp. 1-15.
Title: Positive solutions for a class of quasilinear singular equations
Authors: Jose Valdo Goncalves (Univ. de Brasilia, Brasil)
Carlos Alberto P. Santos (Univ. Federal de Goias, Brasil)
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 $u > 0$ and $u(x)\to 0$ as $|x| \to \infty$.
Here $1 < p < \infty$, $N \geq 3$, $\Delta_{p}$ 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.