On the Solvability of a Class of Operator Differential Equations of the Second Order on the Real Axis

Abstract

Solvability of the operator differential equation of the second order with variable coe cients 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 coeffiients 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.