Boundary Value Problems
Volume 2007 (2007), Article ID 23108, 12 pages
doi:10.1155/2007/23108

Positive solutions for two-point semipositone right focal eigenvalue problem

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.