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

Yuguo Lin and Minghe Pei

 Department of Mathematics, Bei Hua University, JiLin City 132013, China
Received 28 March 2007; Revised 13 July 2007; Accepted 27 August 2007

Recommended by P. Joseph McKenna

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.