[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2016.56.3.819

On the Order of Growth of Solutions to Complex Non-homogeneous Linear Differential Equations

Habib, Habib (Department of Mathematics, Laboratory of Biomathematics, University of Sidi Bel Abbes)
Belaidi, Benharrat (Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB))

Publication Information

Kyungpook Mathematical Journal / v.56, no.3, 2016 , pp. 819-829 More about this Journal

Abstract

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{$ $az}f=F_1e^{az}+F_2e^{bz}$$$ , where $A_j(z)$ ( ${\not\equiv}0$ ) ( $j=0,1,{\cdots},k-1$ ), $F_j(z)$ ( ${\not\equiv}0$ ) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$ .

Keywords

Differential equation; characteristic function; entire function; exponent of convergence of the sequence of zeros; order of growth;

Citations & Related Records

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