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.
Citation
JinRong Wang . W. Wei. X. Xiang. "Bounded and Periodic solutions of a Class of Impulsive Periodic Population Evolution Equations of Volterra type." Commun. Math. Anal. 9 (1) 32 - 47, 2010.
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