Geodesic
A nonlinear integral transform and a global inverse bifurcation theory
Kamimura, Yutaka1
1 Department of Ocean Sciences Tokyo University of Marine Science and Technology 4-5-7 Konan, Minato-ku Tokyo 108-8477, Japan
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 4, pp. 863-911

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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.

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Classification : 44A15, 34A55, 45P05

Kamimura, Yutaka 1

1 Department of Ocean Sciences Tokyo University of Marine Science and Technology 4-5-7 Konan, Minato-ku Tokyo 108-8477, Japan 
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     title = {A nonlinear integral transform and a global inverse bifurcation theory},
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Kamimura, Yutaka. A nonlinear integral transform and a global inverse bifurcation theory. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 4, pp. 863-911. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_4_863_0/