DOI QR코드

DOI QR Code

GROWTH OF SOLUTIONS TO LINEAR DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS OF [p, q]-ORDER IN THE COMPLEX PLANE

  • 투고 : 2017.09.15
  • 심사 : 2017.12.21
  • 발행 : 2018.10.31

초록

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.

키워드

참고문헌

  1. B. Belaidi, On the iterated order and the fixed points of entire solutions of some complex linear differential equations, Electron. J. Qual. Theory Differ. Equ. 2006 (2006), No. 9, 11 pp.
  2. B. Belaidi, Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order, Electron. J. Differential Equations 2009 (2009), No. 70, 10 pp.
  3. B. Belaidi, On the [p, q]-order of meromorphic solutions of linear differential equations, Acta Univ. M. Belii Ser. Math. 23 (2015), 57-69.
  4. L. G. Bernal, On growth k-order of solutions of a complex homogeneous linear differential equation, Proc. Amer. Math. Soc. 101 (1987), no. 2, 317-322. https://doi.org/10.1090/S0002-9939-1987-0902549-5
  5. T.-B. Cao, Complex oscillation of entire solutions of higher-order linear differential equations, Electron. J. Differential Equations 2006 (2006), No. 81, 8 pp.
  6. T.-B. Cao, J.-F. Xu, and Z.-X. Chen, On the meromorphic solutions of linear differential equations on the complex plane, J. Math. Anal. Appl. 364 (2010), no. 1, 130-142. https://doi.org/10.1016/j.jmaa.2009.11.018
  7. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
  8. 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.
  9. 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.
  10. L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), no. 4, 385-405.
  11. I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter Studies in Mathematics, 15, Walter de Gruyter & Co., Berlin, 1993.
  12. 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), no. 1, 55-67. https://doi.org/10.1016/j.jmaa.2010.05.014
  13. J. Tu and Z.-X. Chen, Growth of solutions of complex differential equations with mero- morphic coefficients of finite iterated order, Southeast Asian Bull. Math. 33 (2009), no. 1, 153-164.
  14. J. Tu and C.-F. Yi, On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order, J. Math. Anal. Appl. 340 (2008), no. 1, 487-497. https://doi.org/10.1016/j.jmaa.2007.08.041
  15. L. Yang, Value Distribution Theory, Springer, Berlin, 1993.