Electron. J. Diff. Equ., Vol. 2014 (2014), No. 205, pp. 1-9.

Uniformly finally bounded solutions to systems of differential equations with variable structure and impulses

Katya G. Dishlieva, Angel B. Dishliev

We study nonlinear non-autonomous systems of ordinary differential equations with variable structure and impulses. The consecutive changes on right-hand sides of this system and the impulsive effects on the solution of the corresponding initial problem take place simultaneously at the moment when the solution cancels the switching functions. We find sufficient conditions for the uniform final boundedness of solutions. These results are obtained using a suitable variation of the Lyapunov second method.

Submitted July 17, 2013. Published October 2, 2014.
Math Subject Classifications: 34A37, 65L05.
Key Words: Variable structure; impulses; switching functions; uniformly finally bounded solutions.

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Katya G. Dishlieva
Faculty of Applied Mathematics and Informatics
Technical University of Sofia, Bulgaria
email: kgd@tu-sofia.bg
Angel B. Dishliev
Department of Mathematics
University of Chemical Technology and Metallurgy
Sofia, Bulgaria
email: dishliev@uctm.edu

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