Positive solutions for a class of quasilinear singular equations

Goncalves, Jose Valdo ; Santos, Carlos Alberto P.

Electronic Journal of Differential Equations, Tome 2004 (2004).

Résumé

Summary: 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.

Détail

Classification : 35B40, 35J25, 35J60
Keywords: singular equations, radial positive solutions, fixed points, shooting method