Geodesic
Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations
Communications in Mathematics, Tome 23 (2015) no. 2, pp. 143-161
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 30D35, 34M10
Keywords: Linear differential equations; Meromorphic functions; Exponent of convergence of the sequence of zeros 
@article{COMIM_2015_23_2_a4,
     author = {Belaidi, Benharrat and Latreuch, Zinel\^aabidine},
     title = {Zeros of {Solutions} and {Their} {Derivatives} of {Higher} {Order} {Non-homogeneous} {Linear} {Differential} {Equations}},
     journal = {Communications in Mathematics},
     pages = {143--161},
     year = {2015},
     volume = {23},
     number = {2},
     mrnumber = {3436682},
     zbl = {1343.34202},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2015_23_2_a4/}
}
TY  - JOUR
AU  - Belaidi, Benharrat
AU  - Latreuch, Zinelâabidine
TI  - Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations
JO  - Communications in Mathematics
PY  - 2015
SP  - 143
EP  - 161
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/COMIM_2015_23_2_a4/
LA  - en
ID  - COMIM_2015_23_2_a4
ER  - 
%0 Journal Article
%A Belaidi, Benharrat
%A Latreuch, Zinelâabidine
%T Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations
%J Communications in Mathematics
%D 2015
%P 143-161
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/COMIM_2015_23_2_a4/
%G en
%F COMIM_2015_23_2_a4
Belaidi, Benharrat; Latreuch, Zinelâabidine. Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations. Communications in Mathematics, Tome 23 (2015) no. 2, pp. 143-161. http://geodesic.mathdoc.fr/item/COMIM_2015_23_2_a4/

[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 | Zbl

[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 | MR | Zbl

[3] Belaïdi, B.: Growth and oscillation theory of solutions of some linear differential equations. Mat. Vesnik, 60, 4, 2008, 233-246, | MR | Zbl

[4] Cao, T. B.: Growth of solutions of a class of complex differential equations. Ann. Polon. Math., 95, 2, 2009, 141-152, | DOI | MR | Zbl

[5] Chen, Z. X.: Zeros of meromorphic solutions of higher order linear differential equations. Analysis, 14, 4, 1994, 425-438, | DOI | MR | Zbl

[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 | MR

[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 | MR

[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 | MR | Zbl

[9] Hayman, W. K.: Meromorphic functions. 1964, Clarendon Press, Oxford, | MR | Zbl

[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 | MR | Zbl

[11] Laine, I.: Nevanlinna theory and complex differential equations. 1993, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, | MR

[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 | MR | Zbl

[13] Levin, B. Ya.: Lectures on entire functions. 150, 1996, American Mathematical Society, | MR | Zbl

[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 | MR | Zbl

[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 | MR | Zbl

[16] Wang, L., Liu, H.: Growth of meromorphic solutions of higher order linear differential equations. Electron. J. Differential Equations, 125, 2014, 1-11, | MR | Zbl

[17] Yang, C. C., Yi, H. X.: Uniqueness theory of meromorphic functions. Kluwer Academic Publishers Group, Dordrecht, 557, 2003, | MR | Zbl

[18] Yang, L. Z.: The growth of linear differential equations and their applications. Israel J.Math., 147, 2005, 359-370, | DOI | MR | Zbl