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On Integrable Solutions of Impulsive Delay Differential Equations

L. Berezansky·E. Braverman
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Abstract

The connection of function properties of solutions with exponential stability of linear impulsive differential equation $$\dot{x} (t) - \sum_{k=1}^m {A_k (t) x[h_k(t)]} = r(t),~ t \geq 0, x(ξ) = φ(ξ),~ ξ< 0,$$ $$x(τ_j) = B_j x(τ_j - 0) , ~j=1,2, \dots .$$ The explicit stability results and sufficient conditions for existence of integrable solutions are presented.

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L. Berezansky, E. Braverman. 1994-02-13. On Integrable Solutions of Impulsive Delay Differential Equations. https://arxiv.org/abs/funct-an/9402001

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