Multiple solutions of quasilinear periodic-parabolic inclusions

The existence of multiple solutions for a class of quasilinear periodic-parabolic boundary value problems is proved. Our proof is based on the one hand on the sub–supersolution method for general quasilinear periodic-parabolic inclusions. On the other hand it relies on the construction of non-overlapping ordered intervals of sub–supersolutions by the use of appropriately designed quasilinear elliptic problems and the maximum and anti-maximum principles. Our approach also allows us to provide an elementary existence proof for semilinear periodic-parabolic problems which have been studied otherwise by rather involved and elaborated abstract topological tools.