On subnormal solutions of periodic differential equations (Q624468)

The authors investigate the existence of subnormal solutions and the growth order of all other solutions of the following higher-order linear periodic differential equation \[ f^{(k)}+P_{k-1}(e^{z})f^{(k-1)}+\cdots+P_{0}(e^{z})f=Q_{1}(e^{z})+Q_{2}(e^{-z}), \] and the corresponding homogeneous differential equation \[ f^{(k)}+P_{k-1}(e^{z})f^{(k-1)}+\cdots+P_{0}(e^{z})f=0, \] where \(P_{j}(z)\) \((j=0,\dots,k-1)\) are polynomials in \(z\) such that all constant terms of \(P_{j}(z)\) are equal to zero, \(Q_{1}(z)\) and \(Q_{2}(z)\) are polynomials in \(z\). The obtained results generalize corresponding ones due to Gundersen and Steinbart.