In this paper, we investigate a class of Dirichlet boundary value problems driven by a double-phase operator defined through \(\mathcal {N}\) -functions. We focus on the associated eigenvalue problem and establish a global existence result for nontrivial solutions. The analysis is carried out by variational methods within the framework of Musielak-Orlicz-Sobolev spaces, which naturally accommodate the double-phase structure. Our results extend and complement previous studies on double-phase problems, providing new insights into the interplay between variable growth conditions and eigenvalue parameters.
