Boundary Value Problems
Volume 2007 (2007), Article ID 23108, 12 pages
doi:10.1155/2007/23108
Research Article
Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem
Department of Mathematics, Bei Hua University, JiLin City 132013, China
Received 28 March 2007; Revised 13 July 2007; Accepted 27 August 2007
Academic Editor: P. Joseph McKenna
Copyright © 2007 Yuguo Lin and Minghe 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.
Abstract
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)=λf(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]×[0,∞)p→(−∞,∞) is continuous with f(t,u1,u2,…,up)≥−M for some positive constant M.