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The generalized Bohl–Perron principle for the neutral type vector functional differential equations

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Abstract

We consider a vector homogeneous neutral type functional differential vector equation of a certain class. It is proved that, if the corresponding nonhomogeneous equation with the zero initial conditions and an arbitrary free term bounded on the positive half-line, has a bounded solution, then the considered homogeneous equation is exponentially stable.

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Acknowledgments

I am very grateful to the anonymous reviewers of this paper for their really helpful comments and remarks.

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

    Michael Gil’

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  1. Michael Gil’
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Correspondence to Michael Gil’.

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Gil’, M. The generalized Bohl–Perron principle for the neutral type vector functional differential equations. Math. Control Signals Syst. 25, 133–146 (2013). https://doi.org/10.1007/s00498-012-0100-4

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  • DOI: https://doi.org/10.1007/s00498-012-0100-4

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