Periodic solution for second-order impulsive differential inclusions with relativistic operator

In this paper, the boundary value problem of a second-order impulsive differential inclusion involving a relativistic operator is studied. First, the singular problem is reduced to an equivalent non-singular problem in order to better apply the variational methods. Then the existence of a periodic solution is obtained by nonsmooth critical point theory. Moreover, the boundedness and nonnegativity of solutions are obtained by restricting the discontinuous nonlinear term.