2019
Том 71
№ 11

All Issues

Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis

Radzievskii G. V.

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Abstract

For the equation $L_0x(t)+L_1x′(t) + ... + L_nx^{(n)}(t) = O$, where $L_k, k = 0,1,...,n$, are operators acting in a Banach space, we establish criteria for an arbitrary solution $x(t)$ to be zero provided that the following conditions are satisfied: $x^{(1−1)} (a) = 0, 1 = 1, ..., p$, and $x^{(1−1)} (b) = 0, 1 = 1,...,q$, for $-∞ < a < b < ∞$ (the case of a finite segment) or $x^{(1−1)} (a) = 0, 1 = 1,...,p,$ under the assumption that a solution $x(t)$ is summable on the semiaxis $t ≥ a$ with its first $n$ derivatives.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 3, pp 290-303.

Citation Example: Radzievskii G. V. Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis // Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 279–292.

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