A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities

This paper considers a class of degenerate quasilinear elliptic equations with discontinuous nonlinearities. The existence of positive weak solutions and S-solutions is discussed using variational methods. The results assert that the ( λ , a ) -space of the parameters involved is divided into three regions - no solution, at least one S-solution, and at least two weak solutions (one is S-solution among them), in each region respectively. The regions are separated by a continuous, nondecreasing curve and line segment. Further, there exists an S-solution at each point on the separating curve.