Periodic solutions of parabolic equations with discontinuous nonlinearities

The problem of the existence of periodic solutions for parabolic equations with discontinuous nonlinearities and homogeneous Dirichlet boundary condition is investigated. It is assumed that the coefficients of the differential operator does not depend on time, growth of nonlinearity at infinity is sublinear in the nonresonant case, and it is limited in the resonant case. The operator formulation of the problem reduces to the problem of existence fixed point of a convex-compact maps. Existence theorems of generalized and strong periodic solutions in nonresonant and resonant cases are obtained.