Author: Michele V. Bartuccelli, Jonathan H.B. Deane, Guido Gentile, and Luke Marsh

Title: Invariant sets for the varactor equation
 
Abstract: The differential equation $\ddot{x} + \gamma \dot{x} + x^\mu = f(t)$ with $f(t)$ positive, periodic and continuous is studied. After describing some physical applications of this equation, we construct a variety of invariant sets for it, thereby partitioning the phase plane into regions in which solutions grow without bound and also those in which bounded periodic solutions exist.

Keywords: Dissipative systems; Periodically forced systems; Varactor circuit; Invariant sets; Attracting sets.

Michele Bartuccelli
Department of Mathematics and Statistics
University of Surrey
Guildford, GU2 7HX, UK
e-mail: m.bartuccelli@surrey.ac.uk

Jonathan Deane
Department of Mathematics and Statistics
University of Surrey
Guildford, GU2 7HX, UK
e-mail: j.deane@surrey.ac.uk

Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it

Luke Marsh
Department of Mathematics and Statistics
University of Surrey
Guildford, GU2 7HX, UK
e-mail: l.marsh@surrey.ac.uk