I am looking for a solution to this boundary value problem, or some reference where i can find informations \begin{align*} y''(x) - \varepsilon y''(\pi-x) + \lambda y(x) =0,&\quad 0<x<\pi \\ y(0)=y(\pi)=0, & \quad |\varepsilon|>1,\ \lambda\in\mathbb{R} \end{align*} I tried to make it a system by setting
$$y_1(x)=y(x),\quad y_2(x)=y(\pi-x)$$ this doesn't work for me.