In this paper, we establish the existence of at least one and two positive solutions for the system of higher order boundary value problems by using the Krasnosel'skii fixed point theorem.

Intervals of the parameters 𝜆 and 𝜇 are determined for which there exist positive solutions to the system of dynamic equations

\begin{align*}(-1)^n u^{\Delta^{2n}}(t)+\lambda p(t) f(\upsilon(\sigma(t)))=0, & t\in[a, b],\\ (-1)^n\upsilon^{\Delta^{2n}} (t) + \mu q(t)g (u(\sigma(t))) = 0, & t\in [a, b],\end{align*}

satisfying the Sturm–Liouville boundary conditions

\begin{align*}& \alpha_{i+1}u^{\Delta^{2i}}(a)-\beta_{i+1}u^{\Delta^{2i+1}}(a)=0, \gamma_{i+1}u^{\Delta^{2i}}(\sigma(b))+\delta_{i+1}u^{\Delta^{2i+1}}(\sigma(b))=0,\\ & \alpha_{i+1}\upsilon^{\Delta^{2i}}(a)-\beta_{i+1}\upsilon^{\Delta^{2i+1}}(a)=0,\gamma_{i+1}\upsilon^{\Delta^{2i}}(\sigma(b))+\delta_{i+1}\upsilon^{\Delta^{2i+1}}(\sigma(b))=0,\end{align*}

for $0\leq i\leq n-1$. To this end we apply a Guo–Krasnosel’skii fixed point theorem.