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

Abstract

We consider a resonance problem of the existence of periodic solutions of parabolic equations with discontinuous nonli-nearities and a homogeneous Dirichlet boundary condition. It is assumed that the coefficients of the differential operator do not depend on time, and the growth of the nonlinearity at infinity is linear. The operator formulation of the problem reduces it to the problem of the existence of a fixed point of a convex compact mapping. A theorem on the existence of generalized and strong periodic solutions is proved.