This article is cited in 1 paper

On a Problem for Operator-Differential Second-Order Equations with Nonlocal Boundary Condition

K. A. Kerimov^a, S. S. Mirzoyev<sup>ba

a</sup> Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
^b Baku State University

Abstract: An operator-differential second-order equation with nonlocal boundary condition at zero is considered on the semiaxis. Here we give sufficient conditions on the operator coefficients for the regular solvability of the boundary-value problem. Moreover, we obtain conditions for the completeness and minimality of the derivative of the chain of eigen- and associated vectors generated by the boundary-value problem under study and establish the completeness and minimality of the decreasing elementary solutions of the operator-differential equation under consideration.

Keywords: operator-differential second-order equation, regular solvability of a boundary-value problem, Hilbert space, nonlocal boundary condition.

UDC: 517.95

Received: 24.04.2013

DOI: 10.4213/mzm10305

 English version: Mathematical Notes, 2013, 94:3, 330–334

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