Existence and iteration of positive solutions for one-dimensional p-Laplacian boundary value problems with dependence on the first-order derivative

Authors:
Zhiyong Wang;Jihui Zhang
Affiliations:
Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Jiangsu, Nanjing, China;Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Jiangsu, Nanjing, China
Venue:
Boundary Value Problems
Year:
2008

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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.