# 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} }

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…

## 3 Citations

### Complex oscillation and removable sets

- Mathematics
- 1999

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

- Mathematics
- 2019

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)…

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