Lyapunov-Razumikhin pairs in the instability problem for infinite delay equations |
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Authors: | N.O. Sedova |
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Affiliation: | Department of Mathematics and Information Technology, Ulyanovsk State University, Leo Tolstoi str., 42, 432000 Ulyanovsk, Russia |
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Abstract: | Some theorems on complete instability of the zero solution relative to a set for nonautonomous nonlinear equations with infinite delay are provided. The right-hand side of the equation is assumed to be defined in a fading memory space and to satisfy conditions that allow the construction of limiting equations. We use conceptions of Lyapunov-Razumikhin pairs and limiting equations to obtain new instability results, which are applicable, in particular, to autonomous, periodic and almost periodic in t delay differential equations. |
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Keywords: | 34K20 37B55 |
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