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 .
Citation
Tetsutaro Shibata. "Asymptotic Behavior of the Bifurcation Diagrams for Semilinear Problems with Application to Inverse Bifurcation Problems." Int. J. Differ. Equ. 2015 1 - 11, 2015. https://doi.org/10.1155/2015/138629
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