## 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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