Existence of Solutions for an Impulsive p-laplacian Equation with Nonresonance Conditions

This paper deals with a nonresonance problem given in the shape of a nonlinear impulsive differential equation with Dirichlet boundary conditions. After giving a characterization of the first eigenvalue lambda(1) for an intermediary eigenvalue problem with some properties related to lambda(1) such as simplicity, isolation, strict monotonicity and that the first eigenfunction u(1) which correspond to lambda(1) has a constant sign, also by the characterization of the second eigenvalue lambda(2) and its strictly partial monotonicity, we prove existence of at least one solution to our problem by using variational approach. Finally, we give a few examples to illustrate our main theorems.