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Existence theorems for higher order boundary value problems


Authors: Keith Schrader and S. Umamaheswaram
Journal: Proc. Amer. Math. Soc. 47 (1975), 89-97
DOI: https://doi.org/10.1090/S0002-9939-1975-0352592-4
MathSciNet review: 0352592
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Abstract | References | Additional Information

Abstract: In this paper the differential equation $ {y^{(n)}} = f(x,y)$ and associated boundary conditions $ {y^{(r)}}({x_i}) = {y_{ir}}$ for $ i = 1,2, \cdots ,k$ and $ r = 0,1, \cdots ,\lambda (i) - 1$ where $ \lambda (1) + \lambda (2) + \cdots + \lambda (k) = n$ are considered. Sufficient conditions on $ f$ are given to insure the existence of a solution to this $ k$ point boundary value problem. In the special cases when $ k = 2$ or $ k = 3$ sufficient conditions on $ f$ are given to insure both uniqueness and existence of solutions for certain of the boundary value problems.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0352592-4
Keywords: Nonlinear, boundary value problems, higher order, multipoint
Article copyright: © Copyright 1975 American Mathematical Society

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