Nonexistence of positive solutions of quasilinear elliptic equations with singularity on the boundary in strip-like domains

Pages: 376 - 385, Issue Special, August 2005

 Abstract        Full Text (215.9K)              

Takahiro Hashimoto - Department of Mathematical Sciences, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama-shi, Ehime, Japan 790-77, Japan (email)

Abstract: In this paper, we discuss the nonexistence of positive solutions for nonlinear elliptic equations with singularity on the boundary in infinite strip-like domains. The main results are the nonexistence in eigen-value and sub principal case and they are shown by giving an argument concerning the simplicity of the first eigenvalue for generalized eigenvalue problems combined with translation invariance of the domain. We also show another nonexistence result via a modified version of Pohozaev-type identity.

Keywords:  nonexistence, strip-like domains, singularity.
Mathematics Subject Classification:  Primary: 35J20;Secondary: 35J70.

Received: September 2004;      Revised: April 2005;      Published: September 2005.