Removable Sets in the Oscillation Theory of Complex Differential Equations

@article{Laine1997RemovableSI,
  title={Removable Sets in the Oscillation Theory of Complex Differential Equations},
  author={Ilpo Laine and Shengjian Wu},
  journal={Journal of Mathematical Analysis and Applications},
  year={1997},
  volume={214},
  pages={233-244}
}
  • I. LaineShengjian Wu
  • Published 1 October 1997
  • Mathematics, Philosophy
  • Journal of Mathematical Analysis and Applications
Abstract Letf1, f2be two linearly independent solutions of the linear differential equationf″ + A(z)f = 0, whereA(z) is transcendental entire, and assume that the exponents of convergence for the zero-sequences off1, f2satisfy max(λ(f1), λ(f2)) = ∞. Our main result proves that the zeros ofE ≔ f1f2are uniformly distributed in the sense that quite arbitrary large areas of the complex plane can be removed in such a way that if only zeros outside of these areas will be counted for the exponents of… 
View via Publisher
doi.org
3 Citations
Background Citations
1
Methods Citations
1

Figures from this paper

3 Citations

Complex oscillation and removable sets

Abstract Let A be a transcendental entire function of finite order, and let E be the product of linearly independent solutions of w ″ +  A ( z ) w  = 0. We prove the existence of sequences of annuli…

Borel directions of solutions of a second order linear complex differential equation

Abstract: In this paper, we consider the Borel directions of solutions of the differential equation f ′′ + A(z)f ′ + B(z)f = 0. By using Nevanlinna’s value distribution theory and assuming that A(z)…

Borel Removable Sets in Value Distribution Theory

References

SHOWING 1-10 OF 17 REFERENCES

On the characteristic of functions meromorphic in the unit disk and of their integrals

n(r, F) as the number of poles in ]z] d r and = f r n(t, F) dt N(r, F) J0 $ Then T(r, F) = re(r, F) + N(r, F) is called the Nevanlinna characteristic function of F(z). The function T(r, F ) i s…

Second order differential equations with transcendental coefficients

Soient w 1 et w 2 deux solutions lineairement independantes de w''+Aw=0 ou A est une fonction entiere transcendante d'ordre φ(A)<1. On montre que l'exposant de convergence λ(E) des zeros de E=w 1 w 2…

An estimate of the modulus of the logarithmic derivative of a function which is meromorphic in an angular region, and its application

Remark. If f(z) is meromorphic in the angular region {zi=-~ rl}, it if possible to obtain relations analogous to (i) and (2) by introducing the function it(z)--__ f(ZL/kei=), k-~/(~--=), which is…

On determining the location of complex zeros of solutions of certain linear differential equations

SummaryWe investigate the location of zeros of solutions for a class of second-order linear differential equations. This class had previously been investigated to determine the frequency of zeros of…

On the Frequency of Zeros of Solutions of Second Order Linear Differential Equations

We consider the equation % MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXanrfitLxBI9gBaerbd9wDYLwzYbItLDharqqt%…

On the oscillation theory of $f\sp{\prime\prime}+Af=0$ where $A$ is entire

On the Location of Zeros of Solutions of $f'' + A(z)f = 0$ where $A(z)$ is Entire.

On the real zeros of solutions of f'' + A(z)f = 0 where A(z) is entire

On the distribution of values of meromorphic functions

Nevanlinna Theory and Complex Differential Equations