Sufficient conditions for oscillations of all solutions of a class of impulsive differential equations with deviating argument.

Bainov, D.D.; Dimitrova, M.B.

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Bainov, D.D., Dimitrova, Margarita B., Dishliev, Angel B. (1998)

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This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation $\{\begin{matrix} x^{'} (t) = f (t, x (t), x (α_{1} (t)), \dots, x (α_{n} (t))) for a.e. t \in [0, T], Δ x (t_{k}) = I_{k} (x (t_{k})), k = 1, \dots, m, x (0) = x (T) . \end{matrix}$ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin’s continuation theorem. Examples are presented to illustrate the main results.

Integral inequalities of Gronwall type for piecewise continuous functions.

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