This article is cited in 10 papers

On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order

A. R. Aliev<sup>ab

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

Abstract: We obtain sufficient conditions for the regular solvability of initial boundary-value problems for a class of operator-differential equations of third order with variable coefficients on the semiaxis. These conditions are expressed only in terms of the operator coefficients of the equations under study. We obtain estimates of the norms of intermediate derivative operators via the discontinuous principal parts of the equations and also find relations between these estimates and the conditions for regular solvability.

Keywords: operator-differential equation, self-adjoint operator, initial boundary-value problem, Hilbert space, Banach space, Fourier transform, polynomial operator pencil.

UDC: 517.946

Received: 02.05.2007
Revised: 13.01.2011

DOI: 10.4213/mzm3859

 English version: Mathematical Notes, 2011, 90:3, 307–321

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