In this paper we establish some results of existence of infinitely many solutions for an elliptic equation involving the \(p\)-biharmonic and the \(p\)-Laplacian operators coupled with Navier boundary conditions where the nonlinearities depend on two real parameters and do not satisfy any symmetric condition. The nature of the approach is variational and the main tool is an abstract result of Ricceri. The novelty in the application of this abstract tool is the use of a class of test functions which makes the assumptions on the data easier to verify.