Geodesic
On existence and uniqueness of solutions for ordinary differential equations with nonlinear boundary conditions
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 469-481

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We prove an existence and uniqueness theorem for a nonlinear functional boundary value problem, that is, an ordinary differential equation with a nonlinear boundary condition. The proof is based on a Global Inversion Theorem of Ambrosetti and Prodi, which is applied to the boundary operator restricted to the manifold of the global solutions to the equation. Our result is a generalization of an analogous existence and uniqueness theorem of G. Vidossich, as it is shown with some examples. 
@article{BUMI_2004_8_7B_2_a12,
     author = {Calamai, Alessandro},
     title = {On existence and uniqueness of solutions for ordinary differential equations with nonlinear boundary conditions},
     journal = {Bollettino della Unione matematica italiana},
     pages = {469--481},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {2},
     year = {2004},
     zbl = {1115.34020},
     mrnumber = {MR2072948},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a12/}
}
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Calamai, Alessandro. On existence and uniqueness of solutions for ordinary differential equations with nonlinear boundary conditions. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 469-481. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a12/