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Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance $$x^{\left(n\right)}\left(t\right)=f(t,x\left(t\right),x^{\text{'}}\left(t\right),\cdots ,x^{(n-1)}\left(t\right)),t\in (0,1),x\left(0\right)=\sum _{i=1}^m{\alpha }_{i}x\left({\xi }_i\right),x^{\text{'}}\left(0\right)=\cdots =x^{(n-2)}\left(0\right)=0,x^{(n-1)}\left(1\right)=\sum _{j=1}^l{\beta }_j{x}^{(n-1)}\left({\eta }_j\right),$$ where $f:[0,1]\times {ℝ}^n\to ℝ$ is a Carathéodory function, $0<{\xi }_1<{\xi }_2<\cdots <{\xi }_m<1$, ${\alpha }_i\in ℝ$, $i=1,2,\cdots ,m$, $m\ge 2$ and $0<{\eta }_1<\cdots <{\eta }_l<1$, ${\beta }_j\in ℝ$, $j=1,\cdots ,l$, $l\ge 1$. In this paper, two of the boundary value conditions are responsible for resonance.

In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).