Periodic solutions of a parabolic equation with homogeneous Dirichlet boundary condition and linearly increasing discontinuous nonlinearity

Abstract

We consider a resonance problem of existence of periodic solutions of parabolic equations with discontinuous nonlinearities and homogeneous Dirichlet boundary condition. It is assumed that the coefficients of the differential operator are independent of time and that the growth of nonlinearity at infinity is linear. The operator formulation of the problem reduces it to the problem of existence of fixed point of a convex-valued compact mapping. The theorem on existence of generalized and strong periodic solutions is proved.