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Báo cáo hóa học: " Research Article Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems"

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 Nonlinear nth-Order Singular Nonlocal Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 74517 10 pages doi 10.1155 2007 74517 Research Article Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems Xin an Hao Lishan Liu and Yonghong Wu Received 23 June 2006 Revised 16 January 2007 Accepted 26 January 2007 Recommended by Ivan Kiguradze We study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problems u n t a t f t u 0 t E 0 1 u 0 0 u 0 0 . u n-2 0 0 au n u 1 where 0 n 1 0 ann-1 1. The singularity may appear at t 0 and or t 1. The Krasnosel skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results. Copyright 2007 Xin an Hao et al. 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 this paper we study the existence and multiplicity of positive solutions for the following nth-order nonlinear singular nonlocal boundary value problems BVPs u n t a t f t u 0 t E 0 1 u 0 0 u 0 0 . u n-2 0 0 au n u 1 1.1 where 0 n 1 0 ann-1 1 a maybe singular at t 0 and or t 1. We call a t singular if lim 0- a t TO or limt 1- a t TO. The BVPs for nonlinear differential equations arise in a variety of areas of applied mathematics physics and variational problems of control theory. Many authors have discussed the existence of solutions of second-order or higher-order BVPs for instance 1-4 . Singular BVPs have also been widely studied because of their importance in both practical and theoretical aspects. In many practical problems it is frequent that only positive solutions are useful. There have been many papers available in literature concerning the positive solutions of singular BVPs see 5-9 and references therein. The 2 Boundary Value Problems study of .