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

Jingli Ren1,2 and Weigao Ge3

 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

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+.