Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 612591, 13 pages
http://dx.doi.org/10.5402/2011/612591
Research Article

Positive Solutions for Second-Order Nonlinear Ordinary Differential Systems with Two Parameters

1Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 7 September 2011; Accepted 23 October 2011

Academic Editor: G. C. Georgiou

Copyright © 2011 Lan Sun 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

By using fixed-point theorem and under suitable conditions, we investigate the existence and multiplicity positive solutions to the following systems: 𝑒 ξ…ž ξ…ž ( 𝑑 ) + π‘Ž 𝑒 ( 𝑑 ) + 𝑏 𝑣 ( 𝑑 ) + πœ† β„Ž 1 ( 𝑑 ) 𝑓 ( 𝑒 ( 𝑑 ) , 𝑣 ( 𝑑 ) ) = 0 , 𝑑 ∈ [ 0 , 1 ] , 𝑣 ξ…ž ξ…ž ( 𝑑 ) + 𝑐 𝑒 ( 𝑑 ) + 𝑑 𝑣 ( 𝑑 ) + πœ‡ β„Ž 2 ( 𝑑 ) 𝑔 ( 𝑒 ( 𝑑 ) , 𝑣 ( 𝑑 ) ) = 0 , 𝑑 ∈ [ 0 , 1 ] , 𝑒 ( 0 ) = 𝑒 ( 1 ) = 0 , 𝑣 ( 0 ) = 𝑣 ( 1 ) = 0 , where π‘Ž , 𝑏 , 𝑐 , 𝑑 are four positive constants and πœ† > 0 , πœ‡ > 0 , 𝑓 ( 𝑒 , 𝑣 ) , 𝑔 ( 𝑒 , 𝑣 ) ∈ 𝐢 ( 𝑅 + Γ— 𝑅 + , 𝑅 + ) and β„Ž 1 , β„Ž 2 ∈ 𝐢 ( [ 0 , 1 ] , 𝑅 + ) . We derive two explicit intervals of πœ† and πœ‡ , such that the existence and multiplicity of positive solutions for the systems is guaranteed.