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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2012-01-01
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Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2012/753857 |
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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 |
_version_ |
1716752946454069248 |