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: Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type | Xing and Fu Advances in Difference Equations 2011 2011 14 http content 2011 1 14 RESEARCH o Advances in Difference Equations a SpringerOpen Journal Open Access Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type Yepeng Xing and Yi Fu Correspondence ypxing-jason@ Department of Mathematics Shanghai Normal University 200234 People s Republic of China Abstract In this work we present some new results concerning the existence of solutions for first-order nonlinear integro-differential equations with boundary value conditions. Our methods to prove the existence of solutions involve new differential inequalities and classical fixed-point theorems. MR 2000 Subject Classification. 34D09 34D99. Keywords Boundary value problems integro-differential equations fixed-point motheds 1. Introduction and preliminaries As is known integro-differential equations find many applications in various mathematical problems see Cordunean s book 1 Guo et al. s book 2 and references therein for details. For the recent developments involving existence of solutions to BVPs for integro-differential equations and impulsive integro-differential equations we can refer to 3-17 . So far the main method appeared in the references to guarantee the existence of solutions is the method of upper and low solutions. Motivated by the ideas in the recent works 18 19 we come up with a new approach to ensure the existence of at least one solution for certain family of first-order nonlinear integro-differential equations with periodic boundary value conditions or antiperiodic boundary value conditions. Our methods involve new differential inequalities and the classical fixed-point theory. This paper mainly considers the existence of solutions for the following first-order nonlinear integro-differential system with periodic boundary value conditions. i x f t x Kx t t e 0 1 jx 0 x 1 and first-order .
