Non-homogeneous Linear Differential Equations with Solutions of Finite Order

• Published in: Kyungpook mathematical journal Vol. 45; no. 1; pp. 105 - 114
• Main Author: Belaidi, Benharrat
• Format: Journal Article
• Language: Korean
• Published: 경북대학교 자연과학대학 수학과 01.03.2005
• Subjects: 수학; growth of entire solutions; linear differential equations
• ISSN: 1225-6951; 0454-8124

In this paper we investigate the growth of finite order solutions of the differential equation $f^{(k)}\;+\;A_{k-1}(Z)f^{(k-l)}\;+\;{\cdots}\;+\;A_1(z)f^{\prime}\;+\;A_0(z)f\;=\;F(z)$, where $A_0(z),\;{\cdots}\;,\;A_{k-1}(Z)\;and\;F(z)\;{\neq}\;0$ are entire functions. We find conditions on the coefficients which will guarantees the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. We also estimate the lower bounds of order of solutions if one of the coefficient is dominant in the sense that has larger order than any other coefficients.