## 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.

### MSC:

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