Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 298207 8 pages doi 2009 298207 Research Article Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain Bruno de Andrade and Claudio Cuevas Departamento de Matemdtica Universidade Federal de Pernambuco 50540-740 Recife PE Brazil Correspondence should be addressed to Claudio Cuevas cch@ Received 27 March 2009 Accepted 27 May 2009 Recommended by Simeon Reich We study the existence and uniqueness of almost automorphic resp. pseudo-almost automorphic solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain. Copyright 2009 B. de Andrade and C. Cuevas. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In recent years the theory of almost automorphic functions has been developed extensively see . Bugajewski and N guerekata 1 Cuevas and Lizama 2 and N guerekata 3 and the references therein . However literature concerning pseudo-almost automorphic functions is very new cf. 4 . It is well known that the study of composition of two functions with special properties is important and basic for deep investigations. Recently an interesting article has appeared by Liang et al. 5 concerning the composition of pseudo-almost automorphic functions. The same authors in 6 have applied the results to obtain pseudo-almost automorphic solutions to semilinear differentail equations see also 7 . On the other hand in article by Blot et al. 8 the authors have obtained existence and uniqueness of pseudo-almost automorphic solutions to some classes of partial evolutions equations. In this work we study the existence and uniqueness of almost automorphic and pseudo-almost .