A BOUNDING FUNCTIONS APPROACH TO MULTIVALUED BOUNDARY VALUE PROBLEMS

The solvability of Floquet boundary value problems is investigated for upper-Carathéodory differential inclusions by means of strictly localized C² -bounding functions. The existence of an entirely bounded solution is obtained in a sequential way. Our criteria can be regarded as a multivalued extension of recent results of Mawhin and Thompson concerning periodic and bounded solutions of Carath´eodory differential equations. A simple illustrating example is supplied. Keywords and phrases: Floquet boundary value problems, upper-Carathéodory differential inclusions, bounding functions, bounded solutions.