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On the growth of solutions of some higher order linear differential equations. (English) Zbl 1265.34327
Summary: We discuss the growth of solutions of the higher-order nonhomogeneous linear differential equation \[ f^{(k)}+A_{k-1}f^{(k-1)}+\dotsb +A_2f''+(D_1(z) +A_1(z) e^{az})f'+( D_0(z)+A_0(z) e^{bz}) f=F (k\geq 2), \] where \(a\), \(b\) are complex constants that satisfy \(ab(a-b) \neq 0\) and \(A_j(z)\) \((j=0,1,\dotsc ,k-1)\), \(D_j(z)\) \((j=0,1)\) and \(F(z)\) are entire functions with \(\max \{\rho (A_0),\rho (A_1), \dotsc ,\rho (A_{k-1}),\rho (D_0),\rho (D_1)\}<1\). We also investigate the relationship between small functions and the solutions of the above equation.

34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M03 Linear ordinary differential equations and systems in the complex domain
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