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: EXISTENCE RESULTS FOR SEMILINEAR PERTURBED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONDENSELY DEFINED OPERATORS | EXISTENCE RESULTS FOR SEMILINEAR PERTURBED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONDENSELY DEFINED OPERATORS M. BELMEKKI M. BENCHOHRA AND S. K. NTOUYAS Received 24 January 2006 Revised 9 August 2006 Accepted 5 September 2006 We will establish sufficient conditions for the existence of integral solutions and extremal integral solutions for semilinear functional differential equations with nondensely defined operators in Banach spaces. Copyright 2006 M. Belmekki et al. 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 This paper is concerned with the existence of integral solutions and extremal integral solutions defined on a compact real interval for first-order semilinear differential equations. In Section 3 we consider the following class of semilinear differential equations y t - Ay t f t yt g t yt t e J 0 T y t ộ t t e -r 0 where f g J X C -r 0 E E are given functions A D A c E E is a nondensely defined closed linear operator on E Ộ -r 0 E a given continuous function and E I I a real Banach space. For any function y defined on -r T and any t e J we denote by yt the element of C -r 0 E defined by yt 0 y t Ớ 0 e -r 0 . Here yt represents the history of the state from time t - r up to the present time t. There has been extensive study of semilinear functional differential equations where the operator A generates a C0 semigroup or equivalently when a closed linear operator Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 43696 Pages 1-13 DOI FPTA 2006 43696 2 Perturbed functional differential equations A satisfies i D A E ii the Hille-Yosida condition that is there exist M 0 and T e R such that t to c p A sup AI - T n I AI - A -n I A T n e N M where p A is the resolvent set of A and I is the identity operator. Existence and .
