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The aim of the present paper is to study existence, Osgood type uniqueness and qualitative properties of mild solutions of nonlinear integrodifferential equation with nonlocal condition. The main tools employed in the analysis are based on the applications of the Leray-Schauder alternative, rely on a priori bounds of solutions and the well known Bihari’s integral inequality. AMS Subject Classification: 34A12, 37C25, 34B10

EXISTENCE AND OSGOOD TYPE UNIQUENESS OF MILD SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATION WITH NONLOCAL CONDITION