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On existence and uniqueness of solutions for ordinary differential equations with nonlinear boundary conditions. (English) Zbl 1115.34020
Author’s summary: 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 [J. Differ. Equ. 172, No. 1, 29–41 (2001; Zbl 1003.34016)], as it is shown with some examples.
MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
47J07 Abstract inverse mapping and implicit function theorems involving nonlinear operators
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