Electronic Journal of Differential Equations,
Conference 08 (2002), pp. 9-22

Title: Semi-classical analysis and vanishing properties of
  solutions to quasilinear equations 

Authors: Yves Belaud (Univ. Francois Rabelais, Tours, France)
 
Abstract: 
Let $\Omega$ be an open bounded subset of $\mathbb{R}^N$ 
  and $b$ a measurable nonnegative function in $\Omega$. 
  We deal with the time compact support property for
  $$ u_t - \Delta u + b(x)|u|^{q-1} u  = 0 
  $$ 
  for $p \geq 2$ and 
  $$ u_t - \mathop{\rm div} ( |\nabla u|^{p-2} \nabla u )
     + b(x)|u|^{q-1} u  =  0
  $$ 
  with $m \geq 1$ where $0 \leq q <1$. 
  We give criteria associated to the first eigenvalue of some
  quasilinear Schr\"odinger operators in semi-classical limits. 
  We also provide a lower bound for this eigenvalue. 

Published October 21, 2002.
Math Subject Classifications: 35K55, 35P15.
Key Words: evolution equations; $p$-Laplacian; porous-medium;
 strong absorption; regularizing effects; semi-classical limits.