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

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...

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Main Author: Tetsutaro Shibata
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/753857
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spelling doaj-539b7a730eda46a5b8e54104c36a73d62020-11-24T21:11:43ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/753857753857Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential EquationTetsutaro Shibata0Laboratory of Mathematics, Institute of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, JapanWe 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 .http://dx.doi.org/10.1155/2012/753857
collection DOAJ
language English
format Article
sources DOAJ
author Tetsutaro Shibata
spellingShingle Tetsutaro Shibata
Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation
Abstract and Applied Analysis
author_facet Tetsutaro Shibata
author_sort Tetsutaro Shibata
title Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation
title_short Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation
title_full Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation
title_fullStr Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation
title_full_unstemmed Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation
title_sort asymptotic behavior of bifurcation curve for sine-gordon-type differential equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description 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 .
url http://dx.doi.org/10.1155/2012/753857
work_keys_str_mv AT tetsutaroshibata asymptoticbehaviorofbifurcationcurveforsinegordontypedifferentialequation
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