##### Title: Growth and Complex Oscillation of Linear Differential Equations with Meromorphic Coefficients of [p,q] − ϕ Order

##### Pages: 178-194

##### Cite as:

Rabab Bouabdelli, Benharrat BELAIDI, Growth and Complex Oscillation of Linear Differential Equations with Meromorphic Coefficients of [p,q] − ϕ Order, Int. J. Anal. Appl., 6 (2) (2014), 178-194.#### Abstract

This paper is devoted to considering the growth of solutions of complex higher order linear differential equations with meromorphic coefficients under some assumptions for [p,q] − ϕ order and we obtain some results which improve and extend some previous results of H. Hu and X. M. Zheng; X. Shen, J. Tu and H. Y. Xu and others.

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#### References

- S. Bank, General theorem concerning the growth of solutions of first-order algebraic differential equations, Compositio Math. 25 (1972), 61–70.
- B. Bela¨ıdi, Growth of solutions of linear differential equations in the unit disc, Bull. Math. Analy. Appl., 3 (2011), no. 1, 14–26.
- B. Bela¨ıdi, Growth of solutions to linear differential equations with analytic coefficients of [p, q]-order in the unit disc, Electron. J. Differential Equations 2011, No. 156, 1–11.
- B. Bela¨ıdi, On the [p, q]-order of analytic solutions of linear differential equations in the unit disc, Novi Sad J. Math. 42 (2012), no. 1, 117–129.
- Y. M. Chiang and H. K. Hayman, Estimates on the growth of meromorphic solutions of linear differential equations, Comment. Math. Helv. 79 (2004), no. 3, 451–470.
- I. Chyzhykov, J. Heittokangas and J. R¨atty¨a, Finiteness of ϕ−order of solutions of linear differential equations in the unit disc, J. Anal. Math. 109 (2009), 163–198.
- A. Goldberg and I. Ostrovskii, Value Distribution of Meromorphic functions, Transl. Math. Monogr., vol. 236, Amer. Math. Soc., Providence RI, 2008.
- G. G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1988), no. 1, 415-429.
- W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964.
- H. Hu and X. M. Zheng, Growth of solutions of linear differential equations with meromorphic coefficients of [p, q] −order, Math. Commun. 19(2014), 29-42.
- O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the [p, q]-order and lower [p, q]-order of an entire function, J. Reine Angew. Math. 282 (1976), 53–67.
- O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the [p, q]-type and lower [p, q]-type of an entire function, J. Reine Angew. Math. 290 (1977), 180–190.
- L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), no. 4, 385–405.
- I. Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, 1993.
- L. M. Li and T. B. Cao, Solutions for linear differential equations with meromorphic coeffi- cients of [p, q]-order in the plane, Electron. J. Differential Equations 2012 (2012), No. 195, 1–15.
- J. Liu, J. Tu and L. Z. Shi, Linear differential equations with entire coefficients of [p, q]-order in the complex plane, J. Math. Anal. Appl. 372 (2010), 55–67.
- X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q] − ϕ order, Adv. Difference Equ. 2014 (2014), Article ID 200, 14 pages.
- C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.