Abstract and Applied Analysis
Volume 2012 (2012), Article ID 753857, 16 pages
http://dx.doi.org/10.1155/2012/753857
Research Article

Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation

Tetsutaro Shibata

Laboratory of Mathematics, Institute of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Received 23 October 2012; Accepted 11 December 2012

Academic Editor: Sining Zheng

Copyright © 2012 Tetsutaro Shibata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the nonlinear eigenvalue problems for the equation , , , , where is a parameter. It is known that for a given , there exists a unique solution pair with . We establish the precise asymptotic formulas for bifurcation curve as and to see how the oscillation property of has effect on the behavior of . We also establish the precise asymptotic formula for bifurcation curve    to show the difference between and .