Abstract. We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.
AMSclassification. 34G20, 35K55, 35R70
Keywords. Evolution triple, compact embedding,exremal solution,
measurable multifunction, pseudomonotone map, Kadec-Klee property,
parabolic equation, $p$-Laplacian.