Abstract: The aim of this paper is to discuss the infinitely many solutions of a class of p-biharmonic-like equations on a bounded smooth domain of \bf R^N,where 2pN, and the nonlinearity may not be odd symmetric. Using a recent variational principle of Ricceri, some results of existence of infinitely many solutions are shown, the norms of those solutions tend to zero (to infinity) whenever the nonlinearity oscillates at zero (at infinity).