Boundary Value Problems
Volume 2008 (2008), Article ID 860414, 14 pages
doi:10.1155/2008/860414
Existence and Iteration of Positive Solutions for One-Dimensional p-Laplacian Boundary Value Problems with Dependence on the First-Order Derivative
Zhiyong Wang
and Jihui Zhang
Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Jiangsu, Nanjing 210097, China
Abstract
This paper deals with the existence and iteration of positive solutions for the following one-dimensional p-Laplacian boundary value problems: (ϕp(u′(t)))′+a(t)f(t,u(t),u′(t))=0, t∈(0,1), subject to some boundary conditions. By making use of monotone iterative technique, not only we obtain the existence of positive solutions for the problems, but also we establish iterative schemes for approximating the solutions.