Global and local structures of oscillatory bifurcation curves
Tetsutaro Shibata
Hiroshima University, Higashi-Hiroshima, Japan
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Abstract
We consider the nonlinear eigenvalue problem
where (, ) and is a bifurcation parameter. It is known that, in this case, is parameterized by the maximum norm of the solution associated with and is written as . We show that the bifurcation curve intersects the line infinitely many times by establishing the precise asymptotic formula for as and . We find that, according to the relationship between and , there exist three types of bifurcation curves.
Cite this article
Tetsutaro Shibata, Global and local structures of oscillatory bifurcation curves. J. Spectr. Theory 9 (2019), no. 3, pp. 991–1003
DOI 10.4171/JST/269