R. Srzednicki, ON PERIODIC-SOLUTIONS OF PLANAR POLYNOMIAL DIFFERENTIAL-EQUATIONS WITH PERIODIC COEFFICIENTS, Journal of differential equations, 114(1), 1994, pp. 77-100
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.