Asymptotic analysis of solutions of differential equations with polynomially periodic coefficients (Q1022231)

The authors study the Cauchy problem \[ {dx\over dt}= \Biggl(\sum^\infty_{k=0} A_k(t) t^{m- k}\Biggr)x,\quad x(t_0)= x^0,\;t\geq t_0> 1,\tag{\(*\)} \] where \(A_k(t)\) for \(k\geq 0\) are \(n\times n\)-matrices whose entries are sufficiently smooth and \(T\)-periodic. In the cases \(m=-1\), \(m= 0\), \(m\geq 1\), conditions on the spectrum of the matrix \(A_0\) are derived such that \((*)\) has a unique solution which is bounded for \(t\to+\infty\).