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

Zbl MR
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. 
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/
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     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},
     year = {2004},
     volume = {Ser. 8, 7B},
     number = {2},
     zbl = {1115.34020},
     mrnumber = {MR2072948},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a12/}
}
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