Positive solutions for a system of second-order multi-point boundary value problems (Q434640)

The authors apply the Krasnoselskii fixed point theorem to prove the existence of positive solutions of the nonlinear second order system NEWLINE\[NEWLINE\begin{aligned} u''(t)+\lambda c(t)f(u(t), v(t)) &= 0,\\ v''(t)+\mu d(t)g(u(t), v(t)) &= 0\end{aligned}NEWLINE\]NEWLINE with the multi-point boundary conditions NEWLINE\[NEWLINE\begin{aligned}\alpha x(0)-\beta u'(0) &=0, \quad u(T) =\sum^m_{i=1}\alpha_ia_i u(\xi_i),\\ \gamma x(0)-\delta v'(0) &=0,\quad v(T) =\sum^n_{i=1}\alpha_i b_i v(\eta_i).\end{aligned}NEWLINE\]