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Bounded and Periodic Solutions of a Class of Impulsive Periodic Population Evolution Equations of Volterra Type

Commun. Math. Anal.
Volume 9, Number 1 (2010), 32 - 47

Bounded and Periodic Solutions of a Class of Impulsive Periodic Population Evolution Equations of Volterra Type

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Abstract

This paper deals with a class of impulsive periodic population evolution equations of Volterra type on Banach space. By virtue of integral inequality of Gronwall type for piecewise continuous functions, the prior estimate on the $PC$-mild solutions is derived. The compactness of the new constructed Poincaré operator is shown. This allows us to apply Horn's fixed point theorem to prove the existence of $T_{0}$-periodic $PC$-mild solutions when $PC$-mild solutions are ultimate bounded. At last, an example is given for demonstration.