Abstract :
We consider the planar equation = ∑ ak, l(t) zk l, where ak, l is a T-periodic complex-valued continuous function, equal to 0 for almost all k, l . We present sufficient conditions imposed on ak, l which guarantee the existence of its T-periodic solutions and, in the case a0, 0 = 0, the conditions for the existence of nonzero ones. We use a method which computes the fixed point index of the Poincaré-Andronov operator in isolated sets of fixed points generated by so-called periodic blocks. The method is based on the Lefschetz fixed point theorem and the topological principle Of Wa ewski.
