Nonlinear Analysis 57 (2004) 1029–1041 www.elsevier.com/locate/na Existence and regularity of solutions for some neutral partial dierential equations with nonlocal conditions Khalil Ezzinbi a ; 1; * , Xianlong Fu b; 2 a D epartement de Math ematiques, Facult e des Sciences Semlalia, Universit e Cadi Ayyad, BP 2390, Marrakech, Morocco b Department of Mathematics, East China, Normal University, Shanghai 200062, PR China Received 30 July 2003; accepted 18 March 2004 Abstract In this work, we establish several results about the existence and regularity of solutions for some neutral partial dierential equations with nonlocal conditions. We assume that the linear part generates a strongly continuous semigroup on a general Banach space. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Mild and strict solutions; Neutral partial dierential equations; Nonlocal conditions 1. Introduction In this work, we study the existence and regularity of solutions for neutral partial dierential equations with nonlocal conditions of the following form:    d dt [x(t )-F (t;x(h 1 (t )))]=A[x(t )-F (t;x(h 1 (t )))]+G(t;x(h 2 (t ))); 06t 6a; x(0)+g(x)=x 0 ∈X; (1) where A generates a strongly continuous semigroup (T (t )) t ¿0 on a Banach space X , F;G;g, h 1 and h 2 are given functions to be specied later. * Corresponding author. E-mail address: ezzinbi@ucam.ac.ma (K. Ezzinbi). 1 Supported by TWAS GRANT under contract: No. 03-030 RGMATHS/AF/AC 2 Supported by Mathematics Tianyuan Fund (No. A0324624), NNSF of China (No. 10371040) and Shanghai Priority Academic Discipline. 0362-546X/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2004.03.027