Subnormal solutions of second order nonhomogeneous linear periodic differential equations

We obtain the representations of the subnormal solutions of nonhomogeneous equations [ P 1 ( e z ) + Q 1 ( e - z ) ] f ′ + [ P 2 ( e z ) + Q 2 ( e - z ) ] f = R 1 ( e z ) + R 1 ( e - z ) , P 1 ( z ) , P 2 ( z ) , Q 1 ( z ) , Q 2 ( z ) , R 1 ( z ) and R 2 ( z ) are polynomials in z such that P 1 ( z ) , P 2 ( z ) , Q 1 ( z ) and Q 2 ( z ) are not all constants, deg P 1 ⩽ deg P 2 . We resolve the question raised by Gundersen and Steinbart in 1994.