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

• Main Author: Yves Belaud
• Format: Article
• Language: English
• Published: Texas State University 2002-10-01
• Series: Electronic Journal of Differential Equations
• Subjects: evolution equations; $p$-Laplacian; porous-medium; strong absorption; regularizing effects; semi-classical limits.
• Online Access: http://ejde.math.txstate.edu/conf-proc/08/b1/abstr.html

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 $$ u_t - mathop{m div} ( |abla u|^{p-2} abla u ) + b(x)|u|^{q-1} u = 0 $$ 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.