ON PERIODIC-SOLUTIONS OF PLANAR POLYNOMIAL DIFFERENTIAL-EQUATIONS WITH PERIODIC COEFFICIENTS

We consider the planar equation z=Sigma a(k,t)(t)z(k) ($) over bar z(l ) where a(k,t) is a T-periodic complex-valued continuous function, equ al to 0 for almost all k, l is an element of N. We present sufficient conditions imposed on ak,which guarantee the existence of its T-period ic solutions and, in the case a(0,0) = 0, the conditions for the exist ence of nonzero ones. We use a method which computes the fixed point i ndex of the Poincare-Andronov operator in isolated sets of fixed point s generated by so-called periodic blocks. The method is based on the L efschetz fixed point theorem and the topological principle Of Wazewski . (C) 1994 Academic Press, Inc.