Existence results for semilinear differential equations with nonlocal and impulsive conditions

This paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions. Using the techniques of approximate solutions and fixed point, existence results are obtained, for mild solutions, when the impulsive functions arc only continuous and the nonlocal item is Lipschitz in the space of piecewise continuous functions, is not Lipschitz and not compact, is continuous in the space of Bochner integrable functions, respectively. (c) 2009 Elsevier Inc. All rights reserved.