Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods

► Critical point theory and variational methods are applied to investigate the second order impulsive differential equations. ► The conditions for the existence of multiple solutions are established. ► Main results extend the study, in the sense that we deal with a class of problems that is not considered in related papers. This paper uses critical point theory and variational methods to investigate the multiple solutions of boundary value problems for second order impulsive differential equations. The conditions for the existence of multiple solutions are established. An example is constructed to illustrate the proposed result.