Nonlinear periodic parabolic problems with nonmonotone discontinuities
Dimitrios A. Kandilakis, Νικόλαος Παπαγεωργίου · Proceedings of the Edinburgh Mathematical Society · 1998
In this paper we consider a nonlinear periodic parabolic boundary value problem with a discontinuous nonmonotone nonlinearity. Using a lifting result for operators of type (S+), a general surjectivity theorem for operators of monotone type and an auxiliary problem defined by truncation and penalization we prove the existence of a solution in the order interval formed by an upper and lower solution. Moreover we show that the set of all such solutions is compact in Lp(T, (Z)).