This article is cited in 1 paper

On the solvability of a class of operator differential equations of the second order on the real axis

A. R. Aliev<sup>ab

a</sup> Baku State University, 23 Z. Khalilov Str., Baku, AZ-1148, Azerbaijan
^b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 9 F. Agaev Str., Baku, AZ-1141, Azerbaijan

Abstract: Solvability of the operator dierential equation of the second order with variable coefficients on the real axis in a certain weight space is studied. The main part of the equation is an abstract elliptic equation in Hilbert space. We note that sufficient conditions on operator coefficients of the perturbed part, preserving ellipticity of the equation, are found in the paper, and estimations of the norms of intermediate derivative operators via the main part of the operator differential equation in a certain weight space are also obtained.

Key words and phrases: operator diffeerential equation, selfadjoint operator, discontinuous coefficient, regular solution, Hilbert space.

MSC: 47E05, 34B05

Received: 15.12.2005

Language: English

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