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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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Keywords: Boundary value problems, nonlinear boundary conditions, Nagumo condition, funnel, funnel cross-section
Article copyright: © Copyright 1971 American Mathematical Society

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