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Man’ko, S. N.
Published in
Russian Mathematics

This work is devoted to solving some classes of operator equations, based on the solution of auxiliary one-parameter family of equations, which is obtained fromthe original operator equation by formal replacement of the operator of the integrated parameter. Solutions are vector-valued functions represented by power series or integral. We investigat...

Mishin, S. N.
Published in
Russian Mathematics

We describe a general method that allows us to find solutions to homogeneous differential-operator equations with variable coefficients by means of continuous vector-valued functions. The “homogeneity” is not interpreted as the triviality of the right-hand side of an equation. It is understood in the sense that the left-hand side of an equation is ...

Aksyonov, N. A.
Published in
Russian Mathematics

In this paper we describe a method that allows one to study boundary-value problems for the first-order differential-operator equations in an arbitrary locally convex space.

Kasyanov, P. O. Zadoyanchuk, N. V. Yasinsky, V. V.
Published in
Cybernetics and Systems Analysis

The existence of periodic solutions is constructively substantiated for a class of nonlinear hyperbolic evolution equations. A priori estimates are obtained. Examples are given to illustrate the results.