Strictly localized bounding functions and Floquet boundary value problems

Abstract

Semilinear multivalued equations are considered, in separable Banach spaces with the Radon-Nikodym property. An effective criterion for the existence of solutions to the associated Floquet boundary value problem is showed. Its proof is obtained combining a continuation principle with a Liapunov-like technique and a Scorza-Dragoni type theorem. A strictly localized transversality condition is assumed. The employed method enables to localize the solution values in a not necessarily invariant set; it allows also to introduce nonlinearities with superlinear growth in the state variable.

Keywords

• multivalued boundary value problems
• differential inclusions in banach spaces
• bound sets
• floquet problems
• scorza-dragoni type results