Graef, John R.; Henderson, Johnny; Yang, Bo Positive solutions to a singular third order nonlocal boundary value problem. (English) Zbl 1168.34317 Indian J. Math. 50, No. 2, 317-330 (2008). Summary: The existence of a positive solution is shown for the third-order nonlocal boundary value problem\[ \begin{aligned} y'''&= f(x,y), \quad 0<x\leq 1,\\ y(0)&= y'(p)= \int_q^1 w(x)y''(x)\,dx=0, \end{aligned} \]where \(\frac12<p<q<1\) are fixed, and where \(f(x,y)\) is singular at \(x=0\), \(y=0\), and possibly at \(y=\infty\). The method involves a fixed point theorem for operators that are describing 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 34B16 Singular nonlinear boundary value problems for ordinary differential equations PDFBibTeX XMLCite \textit{J. R. Graef} et al., Indian J. Math. 50, No. 2, 317--330 (2008; Zbl 1168.34317)