Electron. J. Diff. Eqns., Vol. 2008(2008), No. 111, pp. 1-11.

Positive solutions for an m-point boundary-value problem

Le Xuan Truong, Le Thi Phuong Ngoc, Nguyen Thanh Long

Abstract:
In this paper, we obtain sufficient conditions for the existence of a positive solution, and infinitely many positive solutions, of the m-point boundary-value problem
$$\displaylines{ x''(t) = f(t, x(t)), \quad 0 < t < 1, \cr x'(0) = 0, \quad x(1)=\sum_{i=1}^{m-2}\alpha _{i}x(\eta _{i})\,. }$$
Our main tools are the Guo-Krasnoselskii's fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.

Submitted April 22, 2008. Published August 15, 2008.
Math Subject Classifications: 34B07, 34B10, 34B18, 34B27.
Key Words: Multi-point boundary; positive solution; Guo-Krasnoselskii fixed point theorem.

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Le Xuan Truong
University of Technical Education in HoChiMinh City 01 Vo Van Ngan Str., Thu Duc Dist.,
HoChiMinh City, Vietnam
email: lxuantruong@gmail.com
Le Thi Phuong Ngoc
Nhatrang Educational College, 01 Nguyen Chanh Str. Nhatrang City, Vietnam
email: ngoc1966@gmail.com
Nguyen Thanh Long
Department of Mathematics and Computer Science
University of Natural Science, Vietnam National University HoChiMinh City
227 Nguyen Van Cu Str., Dist. 5, HoChiMinh City, Vietnam
email: longnt@hcmc.netnam.vn, longnt2@gmail.com

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