TAILIEUCHUNG - Báo cáo hóa học: " Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions"

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 Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 41589 13 pages doi 2007 41589 Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions Chuanzhi Bai and Dandan Yang Received 12 February 2007 Revised 19 March 2007 Accepted 13 April 2007 Recommended by Kanishka Perera We are concerned with the nonlinear second-order impulsive periodic boundary value problem u t f t u t u t t e 0 T t1 u t u t- I u t1 u t u t- J u t1 u 0 u T u 0 u T new criteria are established based on Schaefer s fixed-point theorem. Copyright 2007 C. Bai and D. 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. 1. Introduction Impulsive differential equations which arise in physics population dynamics economics and so forth are important mathematical tools for providing a better understanding of many real-world models we refer to 1-5 and the references therein. About the applications of the theory of impulsive differential equations to different areas for example see 6-15 . Boundary value problems BVPs for impulsive differential equations and impulsive difference equations 16-20 have received special attention from many authors in recent years. Recently Chen et al. in 21 study the following first-order impulsive nonlinear periodic boundary value problem x t f t x t e 0 N t t1 x t x t- I1 x t1 x 0 x T where N 0 t1 e 0 N t1 is fixed f 0 N X R R is continuous on t u e 0 N t1 X R and the impulse at t t1 is given by a continuous function I1 R R . They 2 Boundary Value Problems investigate the existence of solutions to the problem by means of differential inequalities and Schaefer fixed point theorem. Their results complement and extend those of 22 23 in the sense that they allow superlinear growth of the nonlinearity of

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