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Transactions of the American Mathematical Society

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Two point boundary value problems for nonlinear functional differential equations

Authors: Paul Waltman and James S. W. Wong
Journal: Trans. Amer. Math. Soc. 164 (1972), 39-54
MSC: Primary 34.75
MathSciNet review: 0287126
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Abstract: This paper is concerned with the existence of solutions of two point boundary value problems for functional differential equations. Specifically, we consider

$\displaystyle y'(t) = L(t,{y_t}) + f(t,{y_t}),\quad M{y_a} + N{y_b} = \psi ,$

where M and N are linear operators on $ C[0,h]$. Growth conditions are imposed on f to obtain the existence of solutions. This result is then specialized to the case where $ L(t,{y_t}) = A(t)y(t)$, that is, when the reduced linear equation is an ordinary rather than a functional differential equation. Several examples are discussed to illustrate the results.

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Keywords: Functional differential equations, boundary value problems, periodic solutions, shooting methods, Fredholm alternative
Article copyright: © Copyright 1972 American Mathematical Society