Previous |  Up |  Next

Article

Keywords:
Linear differential equations; Meromorphic functions; Exponent of convergence of the sequence of zeros
Summary:
This paper is devoted to studying the growth and oscillation of solutions and their derivatives of higher order non-homogeneous linear differential equations with finite order meromorphic coefficients. Illustrative examples are also treated.
References:
[1] Bank, S., Laine, I.: On the oscillation theory of $f''+Af=0$ where $A$ is entire. Trans. Amer. Math. Soc., 273, 1, 1982, 351-363, MR 0664047 | Zbl 0505.34026
[2] Bank, S., Laine, I.: On the zeros of meromorphic solutions of second order linear differential equations. Comment. Math. Helv., 58, 4, 1983, 656-677, DOI 10.1007/BF02564659 | MR 0728459 | Zbl 0532.34008
[3] Belaïdi, B.: Growth and oscillation theory of solutions of some linear differential equations. Mat. Vesnik, 60, 4, 2008, 233-246, MR 2465805 | Zbl 1274.30112
[4] Cao, T. B.: Growth of solutions of a class of complex differential equations. Ann. Polon. Math., 95, 2, 2009, 141-152, DOI 10.4064/ap95-2-5 | MR 2476609 | Zbl 1173.34054
[5] Chen, Z. X.: Zeros of meromorphic solutions of higher order linear differential equations. Analysis, 14, 4, 1994, 425-438, DOI 10.1524/anly.1994.14.4.425 | MR 1310623 | Zbl 0815.34003
[6] Chen, Z. X., Gao, S. A.: The complex oscillation theory of certain nonhomogeneous linear differential equations with transcendental entire coefficients. J. Math. Anal. Appl., 179, 2, 1993, 403-416, DOI 10.1006/jmaa.1993.1359 | MR 1249828
[7] Chen, Z. X., Yang, C. C.: Some further results on the zeros and growths of entire solutions of second order linear differential equations. Kodai Math. J., 22, 2, 1999, 273-285, DOI 10.2996/kmj/1138044047 | MR 1700597
[8] Gundersen, G. G., Steinbart, E. M., Wang, S.: The possible orders of solutions of linear differential equations with polynomial coefficients. Trans. Amer. Math. Soc., 350, 3, 1998, 1225-1247, DOI 10.1090/S0002-9947-98-02080-7 | MR 1451603 | Zbl 0893.34003
[9] Hayman, W. K.: Meromorphic functions. 1964, Clarendon Press, Oxford, MR 0164038 | Zbl 0115.06203
[10] Hellerstein, S., Miles, J., Rossi, J.: On the growth of solutions of certain linear differential equations. Ann. Acad. Sci. Fenn. Ser. A I Math., 17, 2, 1992, 343-365, DOI 10.5186/aasfm.1992.1723 | MR 1190329 | Zbl 0759.34005
[11] Laine, I.: Nevanlinna theory and complex differential equations. 1993, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, MR 1207139
[12] Latreuch, Z., Belaïdi, B.: On the zeros of solutions and their derivatives of second order non-homogeneous linear differential equations. Miskolc Math. Notes, 16, 1, 2015, 237-248, DOI 10.18514/MMN.2015.704 | MR 3384603 | Zbl 1340.34344
[13] Levin, B. Ya.: Lectures on entire functions. 150, 1996, American Mathematical Society, MR 1400006 | Zbl 0856.30001
[14] Rubel, L. A., Yang, C. C.: Values shared by an entire function and its derivative. 599, 1977, 101-103, Springer, Berlin, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976). Lecture Notes in Math.. DOI 10.1007/BFb0096830 | MR 0460640 | Zbl 0362.30026
[15] Tu, J., Xu, H. Y., Zhang, C. Y.: On the zeros of solutions of any order of derivative of second order linear differential equations taking small functions. Electron. J. Qual. Theory Differ. Equ., 23, 2011, 1-17, DOI 10.14232/ejqtde.2011.1.23 | MR 2786477 | Zbl 1340.30140
[16] Wang, L., Liu, H.: Growth of meromorphic solutions of higher order linear differential equations. Electron. J. Differential Equations, 125, 2014, 1-11, MR 3210540 | Zbl 1295.30076
[17] Yang, C. C., Yi, H. X.: Uniqueness theory of meromorphic functions. Kluwer Academic Publishers Group, Dordrecht, 557, 2003, MR 2105668 | Zbl 1070.30011
[18] Yang, L. Z.: The growth of linear differential equations and their applications. Israel J.Math., 147, 2005, 359-370, DOI 10.1007/BF02785372 | MR 2166368 | Zbl 1131.34059
Partner of
EuDML logo