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International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 58658, 12 pages
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 ttψ(x,t) is continuous on [0,) for each x(0,ω). We give asymptotic behavior for positive solutions using a potential theory approach.