Nonlinear differentiation equation and analytic function spaces
Hao Li, Songxiao Li

TL;DR
This paper studies a nonlinear complex differential equation, providing conditions for solutions to belong to specific function spaces and establishing growth estimates based on coefficient properties.
Contribution
It introduces new criteria for solutions to be in $Q_K$ spaces and derives growth bounds depending on the coefficients' analytic function spaces.
Findings
Solutions belong to $Q_K$ spaces under certain coefficient conditions
Growth estimates are established for solutions based on coefficient spaces
Provides a link between differential equation solutions and analytic function space properties
Abstract
In this paper we consider the nonlinear complex differential equation where , , are analytic in the unit disk , for all . We investigate this nonlinear differential equation from two aspects. On one hand, we provide some sufficient conditions on coefficients such that all solutions of this equation belong to a class of M\"{o}bius invariant function space, the so-called space. On the other hand, we find some growth estimates for the analytic solutions of this equation if the coefficients belong to some analytic function spaces.
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Taxonomy
TopicsMeromorphic and Entire Functions · Holomorphic and Operator Theory · Analytic and geometric function theory
