Geodesic
Order and hyper-order of entire solutions of linear differential equations with entire coefficients
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we investigate the growth of solutions of the differential equation $$ f^{(k)}+A_{k-1}( z)f^{( k-1) }+\dots+A_{1}(z) f'+A_{0}(z) f=0, $$ where $A_{0}( z) ,\dots, A_{k-1}(z)$ are entire functions with $A_{0}(z) \not\equiv 0$. We will show that if the coefficients satisfy certain growth conditions, then every finite order solution of the equation will satisfy certain other growth conditions. We will also find conditions on the coefficients so that every solution $f\not\equiv 0$ will have infinite order and we estimate in one case the lower bounds of the hyper-order.
Classification : 30D35, 34M10, 34C11
Keywords: linear differential equations, growth of entire functions, hyper-order 
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     author = {Bela{\"\i}di, Benharrat and Hamani, Karima},
     title = {Order and hyper-order of entire solutions of linear differential equations with entire coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a63/}
}
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Belaïdi, Benharrat; Hamani, Karima. Order and hyper-order of entire solutions of linear differential equations with entire coefficients. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a63/