Subnormal solutions of second order nonhomogeneous linear periodic differential equations

We obtain the representations of the subnormal solutions of nonhomogeneous equationsf″+[P1(ez)+Q1(e-z)]f′+[P2(ez)+Q2(e-z)]f=R1(ez)+R1(e-z),f″+[P1(ez)+Q1(e-z)]f′+[P2(ez)+Q2(e-z)]f=R1(ez)+R1(e-z),where P1(z),P2(z),Q1(z),Q2(z),R1(z) and R2(z)R2(z) are polynomials in z   such that P1(z),P2(z),Q1(z) and Q2(z)Q2(z) are not all constants, degP1⩽degP2degP1⩽degP2. We resolve the question raised by Gundersen and Steinbart in 1994.