Clarke duality for Hamiltonian systems with nonstandard growth

Abstract

We consider the existence of periodic solutions to Hamiltonian Systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide an applications to the Φ-laplacian type systems. * SECyT-UNRC, FCEyN-UNLPam and UNSL † SECyT-UNRC, FCEyN-UNLPam and CONICET 2010 AMS Subject Classification. Primary: 34C25 Secondary: 34B15