Asif, Naseer Ahmad; Khan, Rahmat Ali; Henderson, Johnny Existence of positive solutions to a system of singular boundary value problems. (English) Zbl 1215.34029 Dyn. Syst. Appl. 19, No. 2, 395-404 (2010). Summary: Existence results for positive solutions of a coupled system of nonlinear singular two point boundary value problems of the type \[ \begin{aligned} -&x'' = p(t)f(t,y(t),x'(t)),\quad t\in (0,1),\\ -&y'' = q(t)g(t,x(t),y'(t)),\quad t\in (0,1),\\ & a_1x(0)-b_1x'(0)=x'(1)=0,\\ & a_2y(0)-b_2y'(0)=y'(1)=0,\end{aligned} \]are established. The nonlinearities \(f,g:[0,1]\times (0,\infty)\to [t,\infty)\) are allowed to be singular at \(x'=0\) and \(y'=0\). The functions \(p,q\in C(0,1)\) are positive on \((0,1)\) and the constants \(a_i,b_i>0\) \((i=1,2)\). An example is included to show the applicability of our result. Cited in 5 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{N. A. Asif} et al., Dyn. Syst. Appl. 19, No. 2, 395--404 (2010; Zbl 1215.34029)