Abstract
In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation \({f^{( k) }+A_{k-1}( z)e^{P_{k-1}( z) }f^{( k-1)}+\cdots+A_{1}( z) e^{P_{1}( z) }f'+A_{0}( z)e^{P_{0}( z) }f=0 ( k\geq 2)}\) , where \({P_{j}( z) ( j=0,1,\cdots,k-1)}\) are nonconstant polynomials such that deg \({P_{j}=n ( j=0,1,\cdots,k-1)}\) and \({A_{j}( z) (\not\equiv 0) ( j=0,1,\cdots,k-1)}\) are meromorphic functions with order \({\rho ( A_{j}) < n ( j=0,1,\cdots,k-1) }\).
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Belaïdi, B. On the Meromorphic Solutions of Linear Differential Equations. Jrl Syst Sci & Complex 20, 41–46 (2007). https://doi.org/10.1007/s11424-007-9003-8
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DOI: https://doi.org/10.1007/s11424-007-9003-8