2001-Luminy conference on Quasilinear Elliptic and Parabolic Equations and Systems
Electron. J. Diff. Eqns., Conf. 08, 2002, pp. 9-22.

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

Yves Belaud

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 $0 \leq q$ less than 1. We give criteria associated to the first eigenvalue of some quasilinear Schrodinger operators in semi-classical limits. We also provide a lower bound for this eigenvalue.

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Yves Belaud
Laboratoire de Mathematiques et Physique Theorique
Faculte des Sciences et Techniques
Universite Francois Rabelais, 37200 Tours
e-mail: belaud@univ-tours.fr

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