Journal of the
Korean Mathematical Society JKMS

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of
the type \begin{align*}\begin{split}-&x''(t)=f(t,y(t)),\;\;\;\; t\in(0,1),\\-&y''(t)=g(t,x(t)),\;\;\;\; t\in(0,1),\\& x(0)=y(0)=0,\,x(1)=\alpha x(\eta),\,y(1)=\alpha y(\eta),\end{split}\end{align*} are obtained. The nonlinearities $f,g:(0,1)\times (0,\infty)\rightarrow (0,\infty)$ are continuous and may be singular at $t=0$, $t=1$, $x=0$, or $y=0$. The parameters $\eta,\,\alpha$ satisfy $\eta\in(0,1)$, $0<\alpha<1/\eta$. An example is provided to illustrate the results.

Keywords: positive solutions, singular system of ordinary differential equations, three-point nonlocal boundary value problem

MSC numbers: 34B16, 34B18