Journal of Inequalities and Applications
Volume 2005 (2005), Issue 3, Pages 289-302
doi:10.1155/JIA.2005.289
Positive solutions of second-order singular boundary value problem with a Laplace-like operator
1Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China
2Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
3Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Received 18 July 2003
Copyright © 2005 Jingli Ren and Weigao Ge. 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
By use of the concavity of solution for an associate boundary value problem, existence criteria of positive solutions are given for the Dirichlet BVP (Φ(u'))'+λa(t)f(t,u)=0, 0<t<1, u(0)=0=u(1), where Φ is odd and continuous with 0<l1≤((Φ(x)−Φ(y))/(x−y))≤l2, a(t)≥0, and f may change sign and be singular along a curve in [0,1]×ℝ+.