American Institute of Mathematical Sciences

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June  2005, 4(2): 283-294. doi: 10.3934/cpaa.2005.4.283

On positive solutions of the elliptic sine-Gordon equation

Goong Chen 1, , Zhonghai Ding 2, and  Shujie Li 3,

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843, United States
2. 

Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, United States
3. 

Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080

Received  April 2004 Revised  November 2004 Published  March 2005

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.
Keywords: variational methods, positive solutions., Elliptic sine-Gordon equation.
Mathematics Subject Classification: Primary:35J20,58E05;Secondary:35Q20,65N3.
Citation: Goong Chen, Zhonghai Ding, Shujie Li. On positive solutions of the elliptic sine-Gordon equation. Communications on Pure and Applied Analysis, 2005, 4 (2) : 283-294. doi: 10.3934/cpaa.2005.4.283
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