Existence of anti-periodic solutions for quasilinear parabolic hemivariational inequalities

In this paper, we consider the problem of the existence of anti-periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator. Using regularized approximating and first eigenfunction methods and the surjectivity result, we prove the existence of solutions for quasilinear parabolic hemivariational inequalities.