In this article, we focus on triple weak solutions for some p-Laplacian type singular elliptic problems with two parameters and mixed boundary conditions. We show the existence of at least three distinct weak solutions by using variational methods, the Hardy inequality and a recently obtained three critical points theorem under suitable assumptions.

The sufficient condition of the existence of solutions to some superlinear p-Laplacian impulsive differential equations with nonhomogeneous Neumann boundary conditions is obtained. We get two theorems via variational methods and corresponding critical-points theorems. To reveal the value of obtained theorems, two examples are presented combining with the Newton-iterative method.