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

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  • Tetsutaro Shibata

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 .

Suggested Citation

  • Tetsutaro Shibata, 2015. "Asymptotic Behavior of the Bifurcation Diagrams for Semilinear Problems with Application to Inverse Bifurcation Problems," International Journal of Differential Equations, Hindawi, vol. 2015, pages 1-11, January.
    • Handle: RePEc:hin:jnijde:138629
    DOI: 10.1155/2015/138629
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