On positive solutions of the elliptic sine-Gordon equation

Goong Chen; Zhonghai Ding; Shujie Li

doi:10.3934/cpaa.2005.4.283

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2005, Volume 4, Issue 2: 283-294. Doi: 10.3934/cpaa.2005.4.283

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On positive solutions of the elliptic sine-Gordon equation

1.
Department of Mathematics, Texas A&M University, College Station, TX 77843
2.
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020
3.
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080

Received: March 31, 2004

Revised: October 31, 2004

Published: May 2005

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Abstract

The aim of this paper is to study positive solutions of the elliptic sine-Gordon equation on a bounded domain with homogeneous Dirichlet boundary condition, which models the steady state of the Josephson $\pi-$junction in superconductivity. The properties of positive solutions are investigated theoretically and numerically.

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Mathematics Subject Classification: Primary:35J20,58E05;Secondary:35Q20,65N30.

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