In applied physics we need to solve the model cusps model to get corresponding stationary solutions of the system called eigenfucnctions. These stationary solutions show the behaviour the system along the cusps point. In fact, the cusp is a singular point occurs at the of intersection of two curves. The abrubt changes occurs the cusps(singular point). The question is what is the best way to solve the eigenvalue problem containing the cusps. Can i use the inverse iteration method to solve the problem? In fact i am not sure about the limitations of the inverse iteration method.