Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 36, pp. 1-9.
Title: Multiplicity of forced oscillations for scalar differential equations
Authors: Massimo Furi (Dept. Math. ``G. Sansone'', Firenze, Italy)
Maria Patrizia Pera (Dept. Math. ``G. Sansone'', Firenze, Italy)
Marco Spadini (Dept. Math. ``G. Sansone'', Firenze, Italy)
Abstract:
We give, via topological methods, multiplicity results for small
periodic perturbations of scalar second order differential
equations. In particular, we show that the equation
$$ \ddot{x} = g(x)+\varepsilon f(t,x,\dot x), $$
where $g$ is $C^1$ and $f$ is continuous and periodic in $t$,
has $n$ forced oscillations, provided that $g$
changes sign $n$ times ($n>1$).
Submitted December 31, 2000. Published May 21, 2001.
Math Subject Classifications: 34C25, 34C60.
Key Words: Forced oscillations; ordinary differential equations;
multiplicity of periodic solutions.