Nonautonomous second order Hamiltonian systems

Martin Schechter

Vol. 251 (2011), No. 2, 431–452

DOI: 10.2140/pjm.2011.251.431

Abstract

We study the existence of periodic solutions for a second order nonautonomous dynamical system. We make no assumptions on the gradient other than continuity. This allows both sublinear and superlinear problems. We also study the existence of nonconstant solutions.

Keywords

Hamiltonian, second order, nonautonomous, critical point, linking, dynamical system, periodic solution

Mathematical Subject Classification 2000

Primary: 35J20, 35J25, 47J30, 49J40, 58E05

Milestones

Received: 4 May 2010

Accepted: 16 November 2010

Published: 3 June 2011

Proposed: Robert Finn