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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 962565, 5 pages
http://dx.doi.org/10.1155/2015/962565
Research Article

On Stability of Linear Barbashin Type Integrodifferential Equations

Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105 Beer Sheva, Israel

Received 22 March 2015; Accepted 7 July 2015

Academic Editor: Juan F. San-Juan

Copyright © 2015 Michael Gil’. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the Barbashin type equation where , , and are given real functions and is unknown. Conditions for the boundedness of solutions of this equation are suggested. In addition, a new stability test is established for the corresponding homogeneous equation. These results improve the well-known ones in the case when the coefficients are differentiable in time. Our approach is based on solution estimates for operator equations. It can be considered as the extension of the freezing method for ordinary differential equations.