Electron. J. Diff. Eqns., Vol. 2001(2001), No. 77, pp. 1-14.

Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains

Jacqueline Fleckinger, Evans M. Harrell II, & Francois de Thelin

We study the asymptotic behavior of positive solutions $u$ of
$$ -\Delta_p u({\bf x})  =  V({\bf x}) u({\bf x})^{p-1}, 
  \quad p greater than 1;\ {\bf x} \in \Omega,$$
and related partial differential inequalities, as well as conditions for existence of such solutions. Here, $\Omega$ contains the exterior of a ball in $\mathbb{R}^N$ $1 less than p less than N$, $\Delta_p$ is the p-Laplacian, and $V$ is a nonnegative function. Our methods include generalized Riccati transformations, comparison theorems, and the uncertainty principle.

Submitted July 2, 2001. Published December 14, 2001.
Math Subject Classifications: 35B40, 35J60, 35J70.
Key Words: p-Laplacian, Riccati, uncertainty principle.

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Jacqueline Fleckinger
CEREMATH & UMR MIP, Universite Toulouse-1
21 allees de Brienne
31000 Toulouse, France
e-mail address: jfleck@univ-tlse1.fr
Evans M. Harrell II
School of Mathematics, Georgia Tech
Atlanta, GA 30332-0160, USA
e-mail address: harrell@math.gatech.edu
Francois de Thelin
UMR MIP, Universite Paul Sabatier
31062 Toulouse, France
e-mail address: dethelin@mip.ups-tlse.fr
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