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Proceedings of the American Mathematical Society

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

 

 

A counterexample in nonlinear boundary value problems


Author: J. W. Heidel
Journal: Proc. Amer. Math. Soc. 34 (1972), 133-137
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1972-0293160-X
MathSciNet review: 0293160
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Abstract: For the boundary value problem $ (1.1), (1.2)$ below where initial value problems of $ (1.1)$ are unique and exist on $ (a,b)$ it is known that global uniqueness on $ (a,b)$ implies global existence on $ (a,b)$ if $ \beta \delta = 0$. It is also known that this is false if $ \beta \delta \ne 0$ and $ \alpha \delta - \beta \gamma = 0$. It is shown here by example that this is also false if $ \beta \delta \ne 0$ and $ \alpha \delta - \beta \gamma \ne 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293160-X
Keywords: Nonlinear boundary value problems, second order differential equations, global uniqueness, global existence
Article copyright: © Copyright 1972 American Mathematical Society