Geodesic
Growth of solutions of higher-order linear differential equations
Electronic Journal of Differential Equations, Tome 2010 (2010).

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Summary: In this article, we study the growth of solutions of the linear differential equation $$ f^{(k)}+(A_{k-1}(z)e^{P_{k-1}(z)}+B_{k-1}(z)) f^{(k-1)}+\dots +(A_0(z)e^{P_0(z)}+B_0(z))f=0, $$ where $k\geq 2$ is an integer, $P_j(z)$ are nonconstant polynomials and $A_j(z), B_j(z)$ are entire functions, not identically zero. We determine the hyper-order of these solutions, under certain conditions.
Classification : 34A20, 30D35
Keywords: linear differential equation, entire function, hyper-order 
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     author = {Hamani, Karima},
     title = {Growth of solutions of higher-order linear differential equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a147/}
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Hamani, Karima. Growth of solutions of higher-order linear differential equations. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a147/