This paper explores a class of nonlinear second-order differential equations characterized by both instantaneous and non-instantaneous impulsive effects. We employ variational methods and critical point theory to investigate the existence and multiplicity of weak solutions. Specifically, we reformulate the problem as the minimization of an energy functional within an appropriate function space. Critical points of this energy function correspond to weak solutions of the impulsive problem under consideration. By imposing distinct growth conditions on the nonlinearities and impulsive functions, we rigorously establish the existence of at least one solution and infinitely many solutions for the considered problem. We present some examples to illustrate our results.
Nesraoui et al. (Wed,) studied this question.