A nonlinear integral transform and a global inverse bifurcation theory
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 4, p. 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.

Published online : 2018-06-21
Classification:  44A15,  34A55,  45P05
@article{ASNSP_2011_5_10_4_863_0,
     author = {Kamimura, Yutaka},
     title = {A nonlinear integral transform and a global inverse bifurcation theory},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {4},
     year = {2011},
     pages = {863-911},
     zbl = {1253.44003},
     mrnumber = {2932896},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2011_5_10_4_863_0}
}
Kamimura, Yutaka. A nonlinear integral transform and a global inverse bifurcation theory. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 4, pp. 863-911. http://www.numdam.org/item/ASNSP_2011_5_10_4_863_0/

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