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Theorems of Conti-Opial type for nonlinear functional-differential equations. (English. Russian original) Zbl 0908.34046
Differ. Equations 33, No. 2, 184-193 (1997); translation from Differ. Uravn. 33, No. 2, 185-194 (1997).
The paper is concerned with the existence of solutions to functional-differential equations \(dx(t)/dt= f(x)(t)\) under the condition \(h(x)= 0\), where \(f: C(I;\mathbb{R}^n)\to L(I; \mathbb{R}^n)\) and \(h: C(I; \mathbb{R}^n)\to \mathbb{R}^n\) are continuous operators, \(I\) is a closed interval of the real axis, \(n\) is a positive integer, and the solution in question \(x:I\to \mathbb{R}^n\) is assumed to be an absolutely continuous vector function satisfying the equation almost everywhere on \(I\) and the above condition. The authors find sufficient conditions for solvability and unique solvability of the stated problem.

34K05 General theory of functional-differential equations
47J05 Equations involving nonlinear operators (general)
34K10 Boundary value problems for functional-differential equations