Electronic Journal of Differential Equations (May 2001)
Multiplicity of forced oscillations for scalar differential equations
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 ($n>1$).