International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 58658, 12 pages
doi:10.1155/2007/58658
Research Article
On the Existence of Positive Solutions of a Nonlinear Differential Equation
Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia
Received 7 October 2006; Revised 20 December 2006; Accepted 5 January 2007
Academic Editor: Thomas P. Witelski
Copyright © 2007 Sonia Ben Othman et al. 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
We study some existence results for the nonlinear
equation (1/A)(Au')'=uψ(x,u) for x∈(0,ω) with different boundary conditions, where ω∈(0,∞],
A is a continuous function on [0,ω), positive and differentiable on (0,ω), and ψ is a nonnegative function on (0,ω)×[0,∞) such that t↦tψ(x,t) is continuous on [0,∞) for each x∈(0,ω). We give asymptotic behavior for positive solutions using a potential theory approach.