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Growth of solutions to linear differential equations with entire coefficients of $\left[ p,q\right]$-order in the complex plane

Nityagopal Biswas|Samten Tamang
대한수학회 (The Korean Mathematical Society)|2018.10|대한수학회논문집 (Communications of the KMS)|제33권 제4호|pp. 1217-1227

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참고문헌

키워드

meromorphic functionentire functionlinear differential equations$[pq]$-order
주제분류수학

초록

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of $\left[ p,q \right]$-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.

Abstract

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of $\left[ p,q \right]$-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.

참고문헌 (15)

  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(9), pp.11~ (2006)
  2. B. Belaidi, "Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order", Electron. J. Differential Equations, 2009(70), pp.10~ (2009)
  3. -order of meromorphic solutions of linear differential equations, "Acta Univ. M. Belii Ser. Math", 2015, 57~69
  4. L. G. Bernal, "On growth k-order of solutions of a complex homogeneous linear differ-ential equation", Proc. Amer. Math. Soc, 101(2), pp.317~322 (1987)
  5. T.-B. Cao, "Complex oscillation of entire solutions of higher-order linear differential equations", Electron. J. Differential Equations, 2006(81), pp.8~ (2006)
  6. T.-B. Cao, "On the meromorphic solutions of linear differential equations on the complex plane", J. Math. Anal. Appl, 364(1), pp.130~142 (2010)
  7. W. K. Hayman, "Meromorphic Functions, Oxford Mathematical Monographs" (1964), Clarendon Press
  8. -order of an entire function, "J. Reine Angew. Math", 1976, 53~67
  9. -type of an entire function, "J. Reine Angew. Math", 1977, 180~190
  10. L. Kinnunen, "Linear differential equations with solutions of finite iterated order", South-east Asian Bull. Math, 22(4), pp.385~405 (1998)
  11. I. Laine, "Nevanlinna Theory and Complex Differential Equations" (1993), Walter de Gruyter & Co.
  12. -order in the complex plane, "J. Math. Anal. Appl", 2010, 55~67
  13. J. Tu, "Growth of solutions of complex differential equations with mero-morphic coefficients of finite iterated order", Southeast Asian Bull. Math, 33(1), pp.153~164 (2009)
  14. J. Tu, "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(1), pp.487~497 (2008)
  15. L. Yang, "Value Distribution Theory" (1993), Springer

관련 논문AI추천

On growth properties of transcendental meromorphic solutions of linear differential equations with entire coefficients of higher orderNityagopal Biswas, Samten Tamang, Sanjib Kumar Datta대한수학회 · 대한수학회논문집2019 · 제34권 제4호Growth and fixed points of meromorphic solutions of higher-order linear differential equationsHong-Xun Yi, Jun-Feng Xu대한수학회 · 대한수학회지2009 · 제46권 제4호On the Order of Growth of Solutions to Complex Nonhomogeneous Linear Differential EquationsBenharrat Belaidi, Habib Habib경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호Growth of solutions of linear differential-difference equations with coefficients having the same logarithmic orderNityagopal Biswas강원경기수학회 · 한국수학논문집2021 · 제29권 제3호Growth order of Meromorphic Solutions of Higher-orderLinear Differential EquationsJunfeng Xu, Zhanliang Zhang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호Growth and meromorphic solutions of complex differential and differential-difference equationsPradip Das, Sujoy Majumder대한수학회 · 대한수학회보2025 · 제62권 제6호

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