Order of growth of solutions of linear complex differential equations when the coefficients have same order

Naveen Mehra; S. K. Chanyal

Order of growth of solutions of linear complex differential equations when the coefficients have same order

Complex Variables 2021-11-30 v1

Authors: Naveen Mehra , S. K. Chanyal

Abstract

This article contains the theorems which shows that when $A(z)=h_1(z)e^{P_1(z)}$ and $B(z)=h_0(z)e^{P_0(z)}$ are of same order,then all the non-trivial solutions of equation $f"+A(z)f'+B(z)f=0$ are of infinite order. Moreover we extend these results to higher order differential equations.

Keywords

linear complex differential equations order of growth infinite order solutions same order coefficients higher order equations

Cite

@article{arxiv.2111.14379,
  title  = {Order of growth of solutions of linear complex differential equations when the coefficients have same order},
  author = {Naveen Mehra and S. K. Chanyal},
  journal= {arXiv preprint arXiv:2111.14379},
  year   = {2021}
}

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