Electronic Journal of Differential Equations, Vol. 2008(2008), No. 165, pp. 1-6. Title: Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions Author: Nguyen Thanh Chung (Quang Binh Univ., Vietnam) Abstract: Using a recent result by Bonanno [2], we obtain a multiplicity result for the quasilinear elliptic problem $$\displaylines{ - \Delta_p u + |u|^{p-2}u = \lambda f(u) \quad \hbox{in } \Omega, \cr |\nabla u|^{p-2} \frac{\partial u}{\partial \nu} = \mu g(u) \quad \hbox{on } \partial\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb R^N$, $N \geq 3$ with smooth boundary $\partial\Omega$, $\frac{\partial}{\partial\nu}$ is the outer unit normal derivative, the functions $f, g$ are $(p-1)$-sublinear at infinity ($1