# zbMATH — the first resource for mathematics

Orders of solutions of an $$n$$-th order linear differential equation with entire coefficients. (English) Zbl 1039.30012
This paper offers two sectorial type conditions which imply that all nontrivial solutions of the complex linear differential equation $$f^{(n)}+A_{n-1}(z)f^{(n-1)}+\cdots+ A_{1}(z)f'+A_{0}(z)f=0$$ with entire coefficients, $$A_{0}(z)\not\equiv 0$$, are of infinite order of growth. These results are straightforward generalizations of the corresponding results in the case $$n=2$$ due to G. Gundersen in [Trans. Am. Math. Soc. 305, 415–429 (1988; Zbl 0634.34004)]. The proofs offered are immediate adaptions of those given by Gundersen.

##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations
order of growth
Full Text: