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.