Relations between solutions of differential equations and small functions (Q417131)

In this paper, the authors use Nevanlinna theory and oscillation theory of meromorphic functions to study the higher order linear differential equations NEWLINE\[NEWLINE f^{(k)}+A_{k-1}(z)f^{(k-1)}+\dots+A_{1}(z)f'+A_{0}(z)f=0, NEWLINE\]NEWLINE where \(A_{k-1}(z),\dots,A_{1}(z)\) and \(A_{0}(z)\) are entire functions of finite order such that if \(A_{j}(z)\not\equiv 0\), then \(\lambda(A_{j})<\sigma(A_{j})\); if \(i\neq j\), then \(\sigma(A_{i}/A_{j})=\max\{\sigma(A_{i}), \sigma(A_{j})\}\). The authors derive some relations between the meromorphic solutions of such an equation and prove that every meromorphic solution and its derivative have infinitely many fixed points.