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

Takahiro Hashimoto

doi:10.3934/proc.2005.2005.376

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2005, Volume 2005: 376-385. Doi: 10.3934/proc.2005.2005.376 open access

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

Takahiro Hashimoto^1,

1.
Department of Mathematical Sciences, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama-shi, Ehime, Japan 790-77

Received: August 31, 2004

Revised: March 31, 2005

Published: August 2005

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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.

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Mathematics Subject Classification: Primary: 35J20;Secondary: 35J70.

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

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