Maroun, Mariette Positive solutions to an \(n\)th order right focal boundary value problem. (English) Zbl 1115.34027 Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 4, 17 p. (2007). Summary: The existence of a positive solution is obtained for the \(n^{th}\) order right focal boundary value problem \[ y^{(n)}=f(x,y), \quad 0 < x \leq 1. \]\[ y^{(i)}(0)=y^{(n-2)}(p)=y^{(n-1)}(1)=0,\quad i=0,\dots, n-3, \] where \(\frac{1} {2}<p<1\) is fixed and where \(f(x,y)\) is singular at \(x=0, y=0\), and possibly at \(y=\infty\). The method applies a fixed-point theorem for mappings that are decreasing with respect to a cone. Cited in 2 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations PDFBibTeX XMLCite \textit{M. Maroun}, Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 4, 17 p. (2007; Zbl 1115.34027) Full Text: DOI EuDML