Nonlinear perturbation of the Mathieu equation
The author reviews the Melnikov method and discusses its applicability to some equations such as \[ \ddot{x}+\omega^2 x+\mu x\cos t+\epsilon \omega^2 (a_0 x-x^2)+\epsilon \mu \dot{x} =0. \] The bifurcation from closed orbits to subharmonic solutions is also discussed.
scientific article; zbMATH DE number 1343239