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On Stability of Linear Barbashin Type Integrodifferential Equations

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  • Michael Gil’

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.

Suggested Citation

  • Michael Gil’, 2015. "On Stability of Linear Barbashin Type Integrodifferential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-5, July.
    • Handle: RePEc:hin:jnlmpe:962565
    DOI: 10.1155/2015/962565
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