# American Institute of Mathematical Sciences

2009, 2009(Special): 349-358. doi: 10.3934/proc.2009.2009.349

## Nonexistence of weak solutions of quasilinear elliptic equations with variable coefficients

 1 Meteorological College, 7-4-81, Asahi0cho, Kashiwa, Chiba, 277-0852, Japan

Received  September 2008 Revised  April 2009 Published  September 2009

In this paper, we are concerned with the following quasilinear elliptic equations:

-div${a(x)|\nabla u|^{p-2}\nabla u$  $=b(x)|u|^(q-2)u$     in $\Omega$
$u(x)$   $= 0$ on $\partial\Omega$

where $\Omega$ is a domain in $\mathbf R^N$ $(N \ge 1)$ with smooth boundary.
When $a$ and $b$ are positive constants, there are many results on the nonexistence of nontrivial solutions for the equation (E).     The main purpose of this paper is to discuss the nonexistence results for (E) with a class of weak solutions under some assumptions on $a$ and $b$.

Citation: Takahiro Hashimoto. Nonexistence of weak solutions of quasilinear elliptic equations with variable coefficients. Conference Publications, 2009, 2009 (Special) : 349-358. doi: 10.3934/proc.2009.2009.349
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