A nonlinear integral transform and a global inverse bifurcation theory

Kamimura, Yutaka

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 4, pp. 863-911.

We consider a nonlinear integral transform and show that the transform acts as a homeomorphism between certain metric spaces of positive functions. We apply the result to the inverse bifurcation problem of determining the nonlinear term of a certain nonlinear Sturm-Liouville problem from its first bifurcating branch, and we establish the well-posedness of the inverse problem. An application to an inverse problem of determining a restoring force from a time-map is also given.

Classification : 44A15, 34A55, 45P05

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