**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