We study the existence of nontrivial solutions for the problem $\Delta u=u$ , in a bounded smooth domain $\Omega\subset\mathbb{R}^\mathbb{N}$ , with a semilinear boundary condition given by ${\partial u}/{\partial\nu}=\lambda u-W(x)g(u)$ , on the boundary of the domain, where $W$ is a potential changing sign, $g$ has a superlinear growth condition, and the parameter $\lambda\in{]}0,\lambda_1]$; $\lambda_1$ is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.