Growth and oscillation theory of non-homogeneous complex differential equations with entire coefficients. (English) Zbl 1165.30355

Summary: We investigate the growth and the complex oscilllation theorey of the linear differential equation \(f^{(k)}+A_{k-1}f^{(k-1)}+\ldots+A_1f'+A_0f=F\), where \(A_0, A_1,\ldots, A_{k-1}\), \(F\not\equiv 0\) are entire functions. We also investigate the relation between the solutions of a pair of non-homogeneous linear differential equations. We improve some results due to the author, S. Abbas and Z. X. Chen, S.A. Gao.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory