Authors’ abstract: The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the \(p(x)\)-biharmonic operator with Navier boundary value conditions. The proof is mainly based on a three critical points theorem due to B. Ricceri [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3084–3089 (2009; Zbl 1214.47079)].