Rapidly and Slowly Oscillating Periodic Solutions of a Delayed Van der Pol Oscillator

摘要

In this paper, we introduce a method to prove existence of several rapidly and slowly oscillating periodic solutions of a delayed Van der Pol oscillator. The proof is a combination of pen and paper analytic estimates, the contraction mapping theorem and a computer program using interval arithmetic. Using this approach we extend some existence results obtained by Nussbaum (Ann Mat Pura Appl 4(101):263-306, 1974).