Landesman-Lazer type conditions and multiplicity results for nonlinear elliptic problems with Neumann boundary values (Q2440473)

The authors study the existence and multiplicity of solutions for the nonlinear elliptic problem with Neumann boundary condition \[ \begin{cases} -\Delta u=\lambda p u +f(x,u) & \text{ in } \;\Omega,\cr \displaystyle \frac{\partial u}{\partial \eta} = \lambda m u +g(x,u) & \text{ on } \;\partial \Omega, \end{cases} \] under non-resonance or resonance conditions using variational methods. It is considered a weighted eigenvalue problem of Steklov type.