Multiplicity of forced oscillations for scalar differential equations

Electronic Journal of Differential Equations

关键词: Forced oscillations;    ordinary differential equations;    multiplicity of periodic solutions.;   

DOI  :  

来源: DOAJ

【 摘 要 】

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 ($n>1$).

【 授权许可】

Unknown