Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations

Benharrat Belaidi; Zinelâabidine Latreuch

Communications in Mathematics (2015)

  • Volume: 23, Issue: 2, page 143-161
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Belaidi, Benharrat, and Latreuch, Zinelâabidine. "Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations." Communications in Mathematics 23.2 (2015): 143-161. <http://eudml.org/doc/276155>.

@article{Belaidi2015,
abstract = {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.},
author = {Belaidi, Benharrat, Latreuch, Zinelâabidine},
journal = {Communications in Mathematics},
keywords = {Linear differential equations; Meromorphic functions; Exponent of convergence of the sequence of zeros; linear differential equations; meromorphic functions; exponent of convergence of the sequence of zeros},
language = {eng},
number = {2},
pages = {143-161},
publisher = {University of Ostrava},
title = {Zeros of Solutions and Their Derivatives of Higher Order Non-homogeneous Linear Differential Equations},
url = {http://eudml.org/doc/276155},
volume = {23},
year = {2015},
}

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
PB - University of Ostrava
VL - 23
IS - 2
SP - 143
EP - 161
AB - 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.
LA - eng
KW - Linear differential equations; Meromorphic functions; Exponent of convergence of the sequence of zeros; linear differential equations; meromorphic functions; exponent of convergence of the sequence of zeros
UR - http://eudml.org/doc/276155
ER -

References

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  1. Bank, S., Laine, I., On the oscillation theory of f ' ' + A f = 0 where A is entire, Trans. Amer. Math. Soc., 273, 1, 1982, 351-363, (1982) Zbl0505.34026MR0664047
  2. Bank, S., Laine, I., 10.1007/BF02564659, Comment. Math. Helv., 58, 4, 1983, 656-677, (1983) Zbl0532.34008MR0728459DOI10.1007/BF02564659
  3. Belaïdi, B., Growth and oscillation theory of solutions of some linear differential equations, Mat. Vesnik, 60, 4, 2008, 233-246, (2008) Zbl1274.30112MR2465805
  4. Cao, T. B., 10.4064/ap95-2-5, Ann. Polon. Math., 95, 2, 2009, 141-152, (2009) Zbl1173.34054MR2476609DOI10.4064/ap95-2-5
  5. Chen, Z. X., 10.1524/anly.1994.14.4.425, Analysis, 14, 4, 1994, 425-438, (1994) Zbl0815.34003MR1310623DOI10.1524/anly.1994.14.4.425
  6. Chen, Z. X., Gao, S. A., 10.1006/jmaa.1993.1359, J. Math. Anal. Appl., 179, 2, 1993, 403-416, (1993) MR1249828DOI10.1006/jmaa.1993.1359
  7. Chen, Z. X., Yang, C. C., 10.2996/kmj/1138044047, Kodai Math. J., 22, 2, 1999, 273-285, (1999) MR1700597DOI10.2996/kmj/1138044047
  8. Gundersen, G. G., Steinbart, E. M., Wang, S., 10.1090/S0002-9947-98-02080-7, Trans. Amer. Math. Soc., 350, 3, 1998, 1225-1247, (1998) Zbl0893.34003MR1451603DOI10.1090/S0002-9947-98-02080-7
  9. Hayman, W. K., Meromorphic functions, 1964, Clarendon Press, Oxford, (1964) Zbl0115.06203MR0164038
  10. Hellerstein, S., Miles, J., Rossi, J., 10.5186/aasfm.1992.1723, Ann. Acad. Sci. Fenn. Ser. A I Math., 17, 2, 1992, 343-365, (1992) Zbl0759.34005MR1190329DOI10.5186/aasfm.1992.1723
  11. Laine, I., Nevanlinna theory and complex differential equations, 1993, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, (1993) MR1207139
  12. Latreuch, Z., Belaïdi, B., 10.18514/MMN.2015.704, Miskolc Math. Notes, 16, 1, 2015, 237-248, (2015) Zbl1340.34344MR3384603DOI10.18514/MMN.2015.704
  13. Levin, B. Ya., Lectures on entire functions, 150, 1996, American Mathematical Society, (1996) Zbl0856.30001MR1400006
  14. Rubel, L. A., Yang, C. C., 10.1007/BFb0096830, 599, 1977, 101-103, Springer, Berlin, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976). Lecture Notes in Math.. (1977) Zbl0362.30026MR0460640DOI10.1007/BFb0096830
  15. Tu, J., Xu, H. Y., Zhang, C. Y., 10.14232/ejqtde.2011.1.23, Electron. J. Qual. Theory Differ. Equ., 23, 2011, 1-17, (2011) Zbl1340.30140MR2786477DOI10.14232/ejqtde.2011.1.23
  16. Wang, L., Liu, H., Growth of meromorphic solutions of higher order linear differential equations, Electron. J. Differential Equations, 125, 2014, 1-11, (2014) Zbl1295.30076MR3210540
  17. Yang, C. C., Yi, H. X., Uniqueness theory of meromorphic functions, Kluwer Academic Publishers Group, Dordrecht, 557, 2003, (2003) Zbl1070.30011MR2105668
  18. Yang, L. Z., 10.1007/BF02785372, Israel J.Math., 147, 2005, 359-370, (2005) Zbl1131.34059MR2166368DOI10.1007/BF02785372

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