Second order differential variational inequalities involving anti-periodic boundary value conditions

This paper deals with a new class of second order nonlinear differential variational inequalities. Firstly, we study the properties of a solution set for a variational inequality by using the KKM technique and a monotonicity property. Then, we prove the existence of solutions to a second order nonlinear differential variational inequality with anti-periodic boundary value conditions not assuming the Lipschitz continuity of the nonlinear term. Our approaches, which are essentially different from previous research methods in differential variational inequalities, are based on the topological degree theory and the Filippov implicit function lemma.