On the sign definiteness of Liapunov functionals and stability of a linear delay equation

L. B. Knyazhishche, Institute of Mathematics, National Academy of Sciences of Belarus, Belarus
V. A. Scheglov, Institute of Mathematics, National Academy of Sciences of Belarus, Belarus

E. J. Qualitative Theory of Diff. Equ., No. 8. (1998), pp. 1-13.

Abstract: In this paper we give a new definition of the positive-definiteness of the Liapunov functional involved in the stability and asymptotic stability investigation. Using this notion we prove Liapunov type theorems and apply these results to the scalar equation $\dot x(t)=b(t)x(t-r(t))$, where $b(t)$ and $r(t)$ may be unbounded.

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