On Amplitude Bounds for Certain Relaxation Oscillations

摘要

Amplitude bounds are obtained for the unique periodic solution of the generalized Lienard equation ẍ+f(x)x˙+g(x)=0, when the functions f(x) and g(x) are restricted suitably. The restrictions are less severe for the lower than for the upper bounds. A class of equations is exhibited which includes the van der Pol equation and satisfies all the restrictions. Numerical results are given for the van der Pol equation.