Order and Hyper-order of Solutions of Second Order Linear Differential Equations

• Published in: Bulletin of the Malaysian Mathematical Sciences Society Vol. 44; no. 2; pp. 1035 - 1056
• Main Authors: Kumar, Sanjay, Saini, Manisha
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01-03-2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Differential equations; Mathematical analysis; Mathematics; Mathematics and Statistics; Order of growth; Complex differential equation; 34M10; 30D35; Entire function; Exponent of convergence; Lower order of growth
• ISSN: 0126-6705; 2180-4206
• DOI: 10.1007/s40840-020-00993-w

We show that all non-trivial solutions of complex differential equation
f
′
′
+
A
(
z
)
f
′
+
B
(
z
)
f
=
0
are of infinite order if coefficients
A
(
z
) and
B
(
z
) are of special type and establish a relation between the hyper-order of these solutions and the orders of coefficients
A
(
z
) and
B
(
z
). We have also extended these results to higher order complex differential equations.