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On a method of estimating derivatives in complex differential equations. (English) Zbl 1052.34084

Summary: By a recent method to estimate the derivatives \(| w^{(k)}(z_i)|\), \(k> 1\), at certain \(a\)-points of a meromorphic function \(w(z)\) in terms of the Ahlfors-Shimizu characteristic and of \(| w'(z_i)|\), we improve some classical results on the growth of meromorphic solutions to certain algebraic differential equations. Moreover, we offer similar results for equations involving inverse derivatives and derivatives of a power \(w^t\) of a meromorphic function \(w\).

MSC:

34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain
30D30 Meromorphic functions of one complex variable (general theory)
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