ON THE EXISTENCE OF SOLUTIONS FOR NONLINEAR PARABOLIC PROBLEMS WITH NONMONOTONE DISCONTINUITIES

In this paper we consider a nonlinear parabolic problem with a discont inuous, nonmonotone nonlinearity. We assume the existence of an upper solution phi and a lower solution psi such that psi less than or equal to phi. Using results from the theory of pseudomono-tone operators an d from the theory of multivalued analysis together with truncation and penalization techniques, we show that there exists at least one solut ion x(t, x) such that psi(t, z) less than or equal to x(t, z) less tha n or equal to phi(t, z) a.e, on T x Z. (C) 1997 Academic Press.