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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A priori bounds for boundary sets


Authors: J. W. Bebernes and Ross Fraker
Journal: Proc. Amer. Math. Soc. 29 (1971), 313-318
MSC: Primary 34.36
MathSciNet review: 0277807
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Abstract: Consider $ y'' = f(t,y,y')$ with boundary conditions $ (0,y(0),y'(0)) \in {S_1},(1,y(1),y'(1)) \in {S_2}$. It is shown that the boundary value problem has a solution for certain boundary sets $ {S_1}$ and $ {S_2}$ which depend on the assumed Nagumo condition for $ f(t,y,y')$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0277807-9
PII: S 0002-9939(1971)0277807-9
Keywords: Boundary value problems, nonlinear boundary conditions, Nagumo condition, funnel, funnel cross-section
Article copyright: © Copyright 1971 American Mathematical Society