Abstract—The existence, uniqueness and continuous dependence of a mild solution of a Cauchy problem for semilinear impulsive first and second orderfunctional differential-equations with nonlocal conditions in general Banach spaces are studied. Methods of fixed point theorems, of a C₀ semigroup of operators and the Banach contraction theorem are applied.

Index Terms—Functional-differential equations,impulsive, mild solution, nonlocal conditions, semilinear.

H. Akça and J. Benbourenane are with Applied Sciences and Mathematics Department, College of Arts and Sciences, Abu Dhabi University, P.O. Box 59911, Abu Dhabi, UAE (e-mail: Haydar.Akca@adu.ac.ae, Jamal.Benbourenane@adu.ac.ae).
V. Covachev is with the Department of Mathematics & Statistics, College of Science, P.O. Box 36, Sultan Qaboos University, Muscat 123, Oman, on leave from the Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria (e-mail: covachev@hotmail.com, valery@squ.edu.om.).

Cite:Haydar Akça, Jamal Benbourenane, and Valéry Covachev, "Existence Theorem for Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions," International Journal of Applied Physics and Mathematics vol. 3, no. 3, pp. 182-187, 2013.