Electron. J. Diff. Eqns., Vol. 2001(2001), No. 36, pp. 1-9.

Multiplicity of forced oscillations for scalar differential equations

Massimo Furi, Maria Patrizia Pera, & Marco Spadini

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 ($n greater than 1$).

Submitted December 31, 2000. Published May 21, 2001.
Math Subject Classifications: 34C25, 34C60.
Key Words: Forced oscillations, ordinary differential equations, multiplicity of periodic solutions.

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Massimo Furi
Dipartimento di Matematica Applicata ``G. Sansone''
Via S. Marta 3, 50139 Firenze, Italy
e-mail: furi@dma.unifi.it
Maria Patrizia Pera
Dipartimento di Matematica Applicata ``G. Sansone''
Via S. Marta 3, 50139 Firenze, Italy
e-mail: pera@dma.unifi.it
Marco Spadini
Dipartimento di Matematica Applicata ``G. Sansone''
Via S. Marta 3, 50139 Firenze, Italy
e-mail: spadini@dma.unifi.it

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