Truong, Le Xuan; Ngoc, Le Thi Phuong; Long, Nguyen Thanh Positive solutions for an m-point boundary-value problem. (English) Zbl 1171.34014 Electron. J. Differ. Equ. 2008, Paper No. 111, 11 p. (2008). Summary: We obtain sufficient conditions for the existence of a positive solution, and infinitely many positive solutions, of the m-point boundary-value problem \[ x''(t) = f(t, x(t)), \quad 0 < t < 1, \]\[ x'(0) = 0, \quad x(1)=\sum_{i=1}^{m-2}\alpha _{i}x(\eta _{i}). \]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. Cited in 4 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B27 Green’s functions for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations 34A45 Theoretical approximation of solutions to ordinary differential equations Keywords:multi-point boundary; positive solution; Guo-Krasnoselskii fixed point theorem PDFBibTeX XMLCite \textit{L. X. Truong} et al., Electron. J. Differ. Equ. 2008, Paper No. 111, 11 p. (2008; Zbl 1171.34014) Full Text: EuDML EMIS