Summary: We consider the semilinear elliptic eigenvalue problem \(- \Delta u = \lambda f(x,u)\) (with homogeneous Dirichlet boundary conditions) on a smooth bounded domain in \(\mathbb{R}^N\) and prove existence of multiple ordered solutions. We use sub- and super-solutions in a weak sense and apply a “three fixed point theorem” due to H. Amann [SIAM Review 18, 620-709 (1976; Zbl 0345.47044)].