Geodesic
Multiplicity of forced oscillations for scalar differential equations
Electronic journal of differential equations, Tome 2001 (2001)
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__a147,
     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},
     year = {2001},
     volume = {2001},
     zbl = {0979.34035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a147/}
}
TY  - JOUR
AU  - Furi,  Massimo
AU  - Pera,  Maria Patrizia
AU  - Spadini,  Marco
TI  - Multiplicity of forced oscillations for scalar differential equations
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a147/
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%A Pera,  Maria Patrizia
%A Spadini,  Marco
%T Multiplicity of forced oscillations for scalar differential equations
%J Electronic journal of differential equations
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%V 2001
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%G en
%F EJDE_2001__2001__a147
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__a147/