Existence of weak solutions for impulsive p-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 $p$-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 $p=2$.