Asymptotic Behavior of the Bifurcation Diagrams for Semilinear Problems with Application to Inverse Bifurcation Problems

Tetsutaro Shibata

International Journal of Differential Equations, 2015, vol. 2015, 1-11

Abstract:

We consider the nonlinear eigenvalue problem , , , , where is a cubic-like nonlinear term and is a parameter. It is known by Korman et al. (2005) that, under the suitable conditions on , there exist exactly three bifurcation branches ( ), and these curves are parameterized by the maximum norm of the solution corresponding to . In this paper, we establish the precise global structures for ( ), which can be applied to the inverse bifurcation problems. The precise local structures for ( ) are also discussed. Furthermore, we establish the asymptotic shape of the spike layer solution , which corresponds to , as .

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJDE/2015/138629.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJDE/2015/138629.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:138629

DOI: 10.1155/2015/138629

Access Statistics for this article

More articles in International Journal of Differential Equations from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().