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 Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces He Yang | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 293410 15 pages doi 2010 293410 Research Article Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces He Yang Department of Mathematics Northwest Normal University Lanzhou 730070 China Correspondence should be addressed to He Yang yanghe256@ Received 29 December 2009 Revised 20 July 2010 Accepted 3 September 2010 Academic Editor Alberto Cabada Copyright 2010 He Yang. 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. By constructing a mixed monotone iterative technique under a new concept of upper and lower solutions some existence theorems of mild ill-periodic L-quasi solutions for abstract impulsive evolution equations are obtained in ordered Banach spaces. These results partially generalize and extend the relevant results in ordinary differential equations and partial differential equations. 1. Introduction and Main Result Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations it is necessary to develop the methods for their solvability. Unfortunately a comparatively small class of impulsive differential equations can be solved analytically. Therefore it is necessary to establish approximation methods for finding solutions. The monotone iterative technique of Lakshmikantham et al. see 1-3 is such a method which can be applied in practice easily. This technique combines the idea of method of upper and lower solutions with appropriate monotone conditions. Recent results by means of monotone iterative method are obtained in 4-7 and the references therein. In this paper by using a
