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 ($n>1$).

Keywords

• Forced oscillations
• ordinary differential equations
• multiplicity of periodic solutions.