Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function $u$, and prove that the set of bifurcation points for the solutions of the system is not ${\sigma{}} $-compact. Then, we deal with a linear system depending on a real parameter ${\lambda{}}>0$ and on a function $u$, and prove that there exists ${{\lambda{}}}^{{_\ast}} $ such that the set of the functions $u$, such that the system admits nontrivial solutions, contains an accumulation point.
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