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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 for Two-Point Semipositone Right Focal Eigenvalue Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 23108 12 pages doi 10.1155 2007 23108 Research Article Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem Yuguo Lin and Minghe Pei Received 28 March 2007 Revised 13 July 2007 Accepted 27 August 2007 Recommended by P. Joseph McKenna Krasnoselskii s fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone right focal eigenvalue problems -1 n-pu n t Xf t u t u t . u p-1 t u i 0 0 0 i p - 1 u i 1 0 p i n - 1 where n 2 1 p n - 1 is fixed f 0 1 X 0 to p -TO to is continuous with f t u1 u2 . Up - M for some positive constant M. Copyright 2007 Y. Lin and M. Pei. 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 In recent years many papers have discussed the existence of positive solutions of right focal boundary value problems see 1-7 . In 2003 Ma 5 established existence results of positive solutions for the fourth-order semipositone boundary value problems u 4 x Xf x u x u x 1.1 u 0 u 0 u 1 u 1 0. Motivated by Agarwal and Wong 8 and Ma 5 the purpose of this article is to generalize and complement Ma s work to nth-order right focal eigenvalue problems -1 n-pu n t Xf t u t u t . u p-1 t 1.2 with boundary conditions u i 0 0 0 i p - 1 u i 1 0 p i n - 1 1.3 2 Boundary Value Problems where n 2 1 p n - 1 is fixed f 0 1 X 0 to p TO to is continuous with f t u1 u2 . Up M for some positive constant M. We say that u t is positive solution of BVP 1.2 1.3 if u t e cn 0 1 is solution of BVP 1.2 1.3 and u ỉ t 0 t e 0 1 i 0 1 . p 1. For other related works with focal boundary value problem we refer to recent contributions ofAgarwal 1 Agarwal et al. 2 Boey and Wong 3 He and Ge 4 and Wong and Agarwal 6 7 . The outline of the paper is as follows in Section 2 we will .
