HIGHER ORDER ANALYSIS ON THE EXISTENCE OF PERIODIC SOLUTIONS IN CONTINUOUS DIFFERENTIAL EQUATIONS VIA DEGREE THEORY.

Recently, the higher order averaging method for studying periodic solutions of both Lipschitz diferential equations and discontinuous piecewise smooth diferential equations was devel- oped in terms of the Brouwer degree theory. Between the Lipschitz and the discontinuous piecewise smooth diferential equations, there is a huge class of diferential equations lacking in a higher order analysis on the existence of periodic solutions, namely, the class of continuous non-Lipschitz diferen- tial equations. In this paper, based on the degree theory for operator equations, we perform a higher order analysis of continuous perturbed diferential equations and derive sufcient conditions for the existence and uniform convergence of periodic solutions for such systems. We apply our results to study continuous non-Lipschitz higher order perturbations of a harmonic oscillator. [ABSTRACT FROM AUTHOR]