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This paper is concerned with the existence of mild solutions for second order semi-linear functional with delay in Banach space . Our analysis is based on the technique of measure of noncompactness and Schauder’s fixed point theorem. An example illustrating the abstract theory is given. 2010 Mathematics Subject Classification: 34G20.

SECOND ORDER SEMILINEAR EVOLUTION EQUATIONS WITH INFINITE DELAY VIA MEASURE OF NONCOMPACTNESS