Geodesic
Multiplicity of forced oscillations for scalar differential equations
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 ($n greater than 1$).
Classification : 34C25, 34C60
Keywords: forced oscillations, ordinary differential equations, multiplicity of periodic solutions 
@article{EJDE_2001__2001__a225,
     author = {Furi, Massimo and Pera, Maria Patrizia and Spadini, Marco},
     title = {Multiplicity of forced oscillations for scalar differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a225/}
}
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Furi, Massimo; Pera, Maria Patrizia; Spadini, Marco. Multiplicity of forced oscillations for scalar differential equations. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a225/