Existence of weak solutions for impulsive pp-Laplacian problem with superlinear impulses

Using the critical point theory we are going to prove the existence of one and then of many weak solutions under subtle conditions for impulsive pp-Laplacian problem. The novice lies in the fact that we do not restrict ourselves to sublinear impulses. We also prove existence of at least one non-positive and one non-negative solution, when p=2p=2.