Nonexistence of weak solutions of quasilinear elliptic equations with variable coefficients

Pages: 349 - 358, Issue Special, September 2009

 Abstract        Full Text (163.1K)              

Takahiro Hashimoto - Meteorological College, 7-4-81, Asahi0cho, Kashiwa, Chiba, 277-0852, Japan (email)

Abstract: 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 $b$.

Keywords:  nonexistence, quasilinear, elliptic equation
Mathematics Subject Classification:  Primary: 35J25; Secondary: 35J20, 35J70

Received: September 2008;      Revised: April 2009;      Published: September 2009.