Chen, Yun; Yan, Baoqiang; Zhang, Lili Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on \(x'\). (English) Zbl 1141.34309 Electron. J. Differ. Equ. 2007, Paper No. 63, 9 p. (2007). Summary: Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem \[ \begin{aligned} & x''(t)+a(t)f(t,x(t),x'(t))=0,\quad 0<t<1,\\ & x'(0)=0,\quad x(1)=\alpha x(\eta),\end{aligned} \]where \(0<\alpha <1\), \(0<\eta<1 \), and \(f\) may change sign and may be singular at \(x=0\) and \(x'=0\). Cited in 1 Document MSC: 34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations Keywords:Asymptotic formulas; \(L^q\)-norm; simple pendulum PDFBibTeX XMLCite \textit{Y. Chen} et al., Electron. J. Differ. Equ. 2007, Paper No. 63, 9 p. (2007; Zbl 1141.34309) Full Text: EuDML EMIS