ON THE EXISTENCE OF EXTREMAL PERIODIC-SOLUTIONS FOR NONLINEAR PARABOLIC PROBLEMS WITH DISCONTINUITIES

We consider a very general second order nonlinear parabolic boundary v alue problem. Assuming the existence of an upper solution phi and a lo wer solution psi satisfying psi less than or equal to phi, we show tha t the problem has extremal periodic solutions in the order interval K = [psi, phi]. Our proof is based on a general surjectivity result for the sum of two operators of monotone type and on truncation and penali zation techniques. In addition we use a result of independent interest which we prove here and which says that the pseudomonotonicity proper ty of A(t,.) can be lifted to its Nemitsky operator. Finally when we i mpose stronger conditions on the data, we show that the extremal solut ions can be obtained with a monotone iterative process. (C) 1996 Acade mic Press, Inc.