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 Positive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 76493 12 pages doi 2007 76493 Research Article Positive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order Differential Equations Shengli Xie and Jiang Zhu Received 23 March 2006 Revised 8 October 2006 Accepted 5 December 2006 Recommended by P. Joseph Mckenna Some existence theorems of the positive solutions and the multiple positive solutions for singular and nonsingular systems of nonlinear fourth-order boundary value problems are proved by using topological degree theory and cone theory. Copyright 2007 S. Xie and J. Zhu. 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 and preliminary Fourth-order nonlinear differential equations have many applications such as balancing condition of an elastic beam which may be described by nonlinear fourth-order ordinary differential equations. Concerning the studies for singular and nonsingular case one can refer to 1-10 . However there are not many results on the system for nonlinear fourthorder differential equations. In this paper by using topological degree theory and cone theory we study the existence of the positive solutions and the multiple positive solutions for singular and nonsingular system of nonlinear fourth-order boundary value problems. Our conclusions and conditions are different from the ones used in 1-10 for single equations. This paper is divided into three sections in Section 2 we prove the existence of the positive solutions and the multiple positive solutions for systems of nonlinear fourthorder boundary value problems with nonlinear singular terms fi t u which may be singular at t 0 t 1. In Section 3 we prove some existence theorems of the positive solutions and the multiple positive solutions for nonsingular system of .
