Using the technique of Brown and Wu [K.J. Brown, T.F. Wu, A semilinear elliptic system involving nonlinear boundary condition and sign changing weight function, J. Math. Anal. Appl. 337 (2008) 1326–1336], we present a note on the paper [T.F. Wu, A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential, Electron. J. Differential Equations 131 (2006) 1–15] by Wu. Indeed, we extend the multiplicity results for a class of semilinear problems to the quasilinear elliptic problems