Energy method for approximate periodic solution of strongly nonlinear nonautonomous systems
The author develops an energy method to obtain necessary and sufficient conditions for the existence and stability of periodic solutions to equations of the form \[ x''+f(x,x',\Omega t)+g(x)=0, \] where \(f\) is periodic with respect to \(t\). The method allows one to get approximate expressions of the solutions. The results are illustrated by numerical experiments.
scientific article; zbMATH DE number 1396393