New existence and multiplicity of solutions for some Dirichlet problems with impulsive effects

In this paper, we obtain some new existence results of solutions for some Dirichlet impulsive differential problems using critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one nontrivial solution or infinitely many solutions, assuming that the nonlinearity is superquadratic and has a sublinear growth. Our results generalize some existing results and our conditions on the potential are rather relaxed and some existing results in the literature are improved.