- Research Article
- Open access
- Published:
On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations
Journal of Inequalities and Applications volume 2007, Article number: 058189 (2007)
Abstract
We investigate properties of the zeros of solutions for higher-order periodic differential equations, and prove that under certain hypotheses, the convergence exponent of zeros of the product of two linearly independent solutions is infinite.
References
Bank SB, Laine I: Representations of solutions of periodic second order linear differential equations. Journal für die Reine und Angewandte Mathematik 1983, 344: 1–21.
Gao S-A: A further result on the complex oscillation theory of periodic second order linear differential equations. Proceedings of the Edinburgh Mathematical Society 1990,33(1):143–158. 10.1017/S0013091500028959
Bank SB, Langley JK: Oscillation theorems for higher order linear differential equations with entire periodic coefficients. Commentarii Mathematici Universitatis Sancti Pauli 1992,41(1):65–85.
Hayman WK: Meromorphic Functions, Oxford Mathematical Monographs. Clarendon Press, Oxford, UK; 1964:xiv+191.
Yang L: Value Distribution Theory and New Research on It, Monographs in Pure and Applied Mathematics. Science Press, Beijing, China; 1982:iv+330.
Gundersen GG: Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. Journal of the London Mathematical Society 1988,37(1):88–104.
Valiron G: Lectures on the General Theory of Integral Functions. Chelsea, New York, NY, USA; 1949.
Chiang Y-M, Gao S-A: On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results. Annales Academiæ Scientiarium Fennicæ. Mathematica 2002,27(2):273–290.
Ince E: Ordinary Differential Equations. Longmans, London, UK; 1927.
Barry PD: On a theorem of Besicovitch. The Quarterly Journal of Mathematics 1963,14(1):293–302. 10.1093/qmath/14.1.293
Barry PD: Some theorems related to thetheorem. Proceedings of the London Mathematical Society 1970,21(2):334–360. 10.1112/plms/s3-21.2.334
Gao SA, Chen ZX, Chen TW: The Complex Oscillation Theory of Linear Differential Equations. Middle China University of Technology Press, Wuhan, China; 1998.
Hayman WK: Angular value distribution of power series with gaps. Proceedings of the London Mathematical Society 1972, 24: 590–624. 10.1112/plms/s3-24.4.590
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Chen, ZX., Gao, SA. On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations. J Inequal Appl 2007, 058189 (2007). https://doi.org/10.1155/2007/58189
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/58189