Growth estimates of solutions of linear differential equations with dominant coefficient of lower $(\alpha ,\beta ,\gamma )$-order

TL;DR

This paper investigates the growth and oscillation behavior of solutions to higher order linear differential equations with a dominant coefficient characterized by lower $(eta ,eta ,eta)$-order, extending previous results in the field.

Contribution

It introduces new conditions based on lower $(eta ,eta ,eta)$-order and type for the dominant coefficient, improving and extending existing theorems on solution behavior.

Findings

Established new growth estimates for solutions.

Derived oscillation criteria under dominant coefficient conditions.

Extended previous results to broader classes of differential equations.

Abstract

In this paper, we deal with the growth and oscillation of solutions of higher order linear differential equations. Under the conditions that there exists a coefficient which dominates the other coefficients by its lower $% (\alpha ,\beta ,\gamma )$-order and lower $(\alpha ,\beta ,\gamma )$-type, we obtain some growth and oscillation properties of solutions of such equations which improve and extend some recently results of the author and Biswas \cite{b8}.