Two point boundary value problems for nonlinear functional differential equations

Waltman, Paul; Wong, James S. W.

doi:10.1090/S0002-9947-1972-0287126-8

Two point boundary value problems for nonlinear functional differential equations
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by Paul Waltman and James S. W. Wong PDF

Trans. Amer. Math. Soc. 164 (1972), 39-54 Request permission

Abstract:

This paper is concerned with the existence of solutions of two point boundary value problems for functional differential equations. Specifically, we consider \[ y’(t) = L(t,{y_t}) + f(t,{y_t}),\quad M{y_a} + N{y_b} = \psi ,\] 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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