Nonlinear Steklov eigenvalues problems

We consider the problem of finding a harmonic function $u$ in a bounded domain $\Omega \subset \mathbf R^N$, $N \geq 2$, satisfying a nonlinear boundary condition of the form $ \partial_{\nu}u(x)=\ lambda \mu(x)h(u(x))$, $x \in \partial \Omega$ where $\mu$ changes sign and $h$ is an increasing function with superlinear, subcritical growth at infinity. We study the solvability of the problem depending on the parameter $\lambda$ by using min-max methods