Relation between differential polynomials and small functions (Q983876)

The authors discuss the growth of solutions of the second-order non-homo\-ge\-ne\-ous differential equation \[ f'' +A_1(z)e^{az} f' +A_0(z)e^{bz} f=F, \] where \(a,b\) are complex numbers and \(A_j(z)\not\equiv 0\) \((j=0,1)\), and \(F\not\equiv 0\) are entire functions such that \(\max \{ \rho(A_0), \rho(A_1), \rho(F)\}<1 \). Slight improvements of the results of \textit{I. Laine} and \textit{J. Wang} [J. Math. Anal. Appl. 342, 39--51 (2008; Zbl 1151.34069)], and \textit{Z. X. Chen} [Sci. China Ser. A 45, No.~3, 290--300 (2002; Zbl 1054.34139)] are obtained. Relations between small functions and some differential polynomials generated by solutions of the equation are studied.