On the Growth of Higher Order Complex Linear Differential Equations Solutions with Entire and Meromorphic Coefficients

We revisit the problem of studying the solutions growth order in complex higher order linear differential equations with entire and meromorphic coefficients of p,q-order, proving how it is related to the growth of the coefficient of the unknown function under adequate assumptions. Our study improves the previous results due to J. Liu - J. Tu - L. Z Shi, L.M. Li - T.B. Cao, and others.

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In this study, we investigate the growth order of solutions in complex higher order linear differential equations with entire and meromorphic coefficients. We show how this growth is related to the growth of the unknown function's coefficients under certain assumptions, and our findings build upon previous results by Liu, Tu, Shi, Li, Cao, and others.