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ON THE SOLVABILITY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

Authors:	Kiguradze I Puza B

Abstract:	Sufficient conditions are established for the solvability of the boundary value problem $\begin{gathered} \frac{{dx(t)}}{{dt}} = p(x,x)(t) + q(x)(t), \hfill \\ l(x,x) = c(x), \hfill \\ \end{gathered}$ where p : C(I; R ⁿ) × C(I; R ⁿ) L(I; R ⁿ), q : C(I; R ⁿ) L(I; R ⁿ), l : C(I, R ⁿ) × C(I; R ⁿ) R ⁿ, and c _n : C(I, R ⁿ) R ⁿ are continuous operators, and p(x, ) and l(x, ) are linear operators for any fixed $x \in C(I;R^n )$ .

Keywords:	Functional differential equation Volterra operator boundary value problem existence theorem
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