×

zbMATH — the first resource for mathematics

On the oscillation of solutions of certain linear differential equations in the complex domain. (English) Zbl 0596.30049
Let A(z) be an entire function of finite order having zero as a Borel exceptional value. Conditions are given on the location of zeros of A(z) which ensure that all non-trivial solutions of \[ y^{(k)}+(A(z)+Q(z))y=0, \] where \(k\geq 2\) and Q is a sufficiently small polynomial, have zeros with infinite exponent of convergence. In particular this is true for all solutions of \(y^{(k)}+e^{P(z)}y=0,\) if \(k\geq 2\) and P is a non-constant polynomial.

MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M99 Ordinary differential equations in the complex domain
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bank, Resultate Math.
[2] DOI: 10.2307/1999210 · Zbl 0505.34026 · doi:10.2307/1999210
[3] Bank, Math. Scand. 40 pp 119– (1977) · Zbl 0367.34004 · doi:10.7146/math.scand.a-11681
[4] DOI: 10.1007/BF01176476 · Zbl 0494.34005 · doi:10.1007/BF01176476
[5] Bellman, Stability Theory of Differential Equations (1953)
[6] DOI: 10.1007/BF01580359 · Zbl 0226.34005 · doi:10.1007/BF01580359
[7] Hayman, Meromorphic Functions (1964)
[8] DOI: 10.1007/BF02565929 · Zbl 0123.26702 · doi:10.1007/BF02565929
[9] Titchmarsh, The Theory of Functions (1949) · Zbl 0035.18001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.