S.B. Waluya, W.T. Van Horssen
In this paper strongly nonlinear oscillator equations will be studied. It will be shown that the recently developed perturbation method based on integrating factors can be used to approximate first integrals. Not only approximations of first integrals will be given, but it will also be shown how in a rather efficient way the existence and stability of time-periodic solutions can be obtained from these approximations. In particular the generalized Rayleigh oscillator equation Ẍ + 9X + μX2 + λX3 = ε(Ẋ - Ẋ3) will be studied in detail, and it will be shown that at least five limit cycles can occur.
Dept. of Appl. Mathematical Analysis, Fac. of Info. Technol. and Systems, Delft University of Technology, 2628 CD Delft, Mekelweg 4, Netherlands; Mathematics Department, Semarang State University, Semarang, Indonesia
