Subnormal Solutions of Second-Order Nonhomogeneous Linear Differential Equations with Periodic Coefficients

Abstract

We obtain the representations of the subnormal solutions of nonhomogeneous linear differential equation f′′+[P1(ez)+Q1(e−z)]f′+[P2(ez)+Q2(e−z)]f=R1(ez)+R2(e−z), where P1(z),P2(z),Q1(z),Q2(z),R1(z), and R2(z) are polynomials in z such that P1(z),P2(z),Q1(z), and Q2(z) are not all constants, deg⁡P1>deg⁡P2. We partly resolve the question raised by G. G. Gundersen and E. M. Steinbart in 1994.