Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 77, pp. 1-14.

Title: Asymptotic behavior of solutions for some nonlinear
       partial differential equations on unbounded domains
   
Authors: Jacqueline Fleckinger (Univ. Toulouse-1, Toulouse, France)
  Evans M. Harrell II (Georgia Inst. of Technology, Atlanta, USA)
  Francois de Thelin (Univ. Paul Sabatier, Toulouse, France)
                 
Abstract:  
 We study the asymptotic behavior of positive solutions $u$ of 
  $$ -\Delta_p u({\bf x})  =  V({\bf x}) u({\bf x})^{p-1}, 
  \quad p>1;\ {\bf x} \in \Omega,$$
 and related partial differential inequalities, as well
 as conditions for existence of such solutions.
 Here, $\Omega$ contains the exterior of a ball in $\mathbb{R}^N$
 $1<p<N$, $\Delta_p$ 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.