Abstract
In this paper, we will study a system of Sturm–Liouville differential equations under the Dirichlet boundary condition. First, by using a three‐critical‐point theorem, we check the existence of at least three weak solutions for the problem, and then, by utilizing a local minimum theorem, we present sufficient conditions so that the existence of at least one nontrivial weak solution for the problem is guaranteed. As an example, it will be mentioned that for λ ∈ (0, 2√e/(e + 1)), the following problem has a weak nontrivial solution.