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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An existence theorem for boundary value problems of nonlinear ordinary differential equations


Author: Gene A. Klaasen
Journal: Proc. Amer. Math. Soc. 61 (1976), 81-84
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1976-0466711-3
MathSciNet review: 0466711
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Abstract: Let $ f$ be continuous on $ (a,b) \times {R^n}$ and suppose solutions of initial value problems for $ {y^{(n)}} = f(t,y, \ldots ,{y^{(n - 1)}})$ exist on $ (a,b)$. Relaxing the assumption that solutions of initial value problems are unique, global existence of solutions of the boundary value problem

$\displaystyle {y^{(n)}} = f(t,y, \ldots ,{y^{(n - 1)}}),y({t_i}) = {\alpha _i}\quad {\text{for }}1 \leqslant i \leqslant n,$

is established assuming uniqueness of solutions of these problems and a compactness property of solutions of the differential equation.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0466711-3
Keywords: Ordinary differential equations, boundary value problems
Article copyright: © Copyright 1976 American Mathematical Society

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