Response solutions of 3-dimensional degenerate quasi-periodic systems with small parameter

Abstract

This paper considers a class of 3-dimensional real analytic nonlinear quasi-periodic systems with a small perturbation parameter, whose unperturbed part has a degenerate equilibrium point. Based on the Leray-Schauder Continuation Theorem [18] , [20] and using technique of outer parameter, we prove that the system has a small response solution for many sufficiently small parameters.