Positive solutions for an m-point boundary-value problem

• Main Authors: Nguyen Thanh Long, Le Thi Phuong Ngoc, Le Xuan Truong
• Format: Article
• Language: English
• Published: Texas State University 2008-08-01
• Series: Electronic Journal of Differential Equations
• Subjects: Multi-point boundary; positive solution; Guo-Krasnoselskii fixed point theorem
• Online Access: http://ejde.math.txstate.edu/Volumes/2008/111/abstr.html

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.