On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique

Abstract

ABSTRACT This paper investigates the limit cycles for planar differential system where are homogeneous polynomials of degree n. Using the method of upper and lower solutions we show that this system has a unique limit cycle under some suitable conditions. Moreover, by employing the monotone iterative technique, we provide a computational method to obtain the expression, or the asymptotical one, of this limit cycle in the polar form. The error estimation of the asymptotical solutions is also provided.