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Complex oscillation of a second order linear differential equation with entire coefficients of (α,β)-order

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Abstrakty
EN
In this paper we study distribution of zeros and growth of solutions of second order linear equations depending on the coefficients of the equation and their (α, β)-order. We obtain results in general form, which considerably extend some results from [21].
Rocznik
Strony
1--21
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria
  • Rajbari, Rabindrapally, R. N. Tagore Road, P.O.- Krishnagar, P.S. Kotwali, Dist-Nadia, PIN-741101, West Bengal, India
Bibliografia
  • 1. Bank S., Laine I.: On the oscillation theory of f00 +Af = 0 where A is entire. Trans. Amer. Math. Soc. 273 (1982), no. 1, 351-363.
  • 2. Bank S., Laine I.: On the zeros of meromorphic solutions of second-order linear differential equations. Comment. Math. Helv. 58 (1983), no. 4, 656-677.
  • 3. Bank S., Laine I., Langley J.: Oscillation results for solutions of linear differential equations in the complex domain. Results Math. 16 (1989), no. 1-2, 3-15.
  • 4. Bela¨ıdi B.: Growth of ρϕ-order solutions of linear differential equations with entire coefficients. PanAmer. Math. J. 27 (2017), no. 4, 26-42.
  • 5. 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 (1999), no. 2, 273-285.
  • 6. Cao T.B., Li L.M.: Oscillation results on meromorphic solutions of second order differential equations in the complex plane. Electron. J. Qual. Theory Differ. Equ. 2010, No. 68, 13 pp.
  • 7. Chyzhykov I., Heittokangas J., Rättyä J.: Finiteness of ϕ-order of solutions of linear differential equations in the unit disc. J. Anal. Math. 109 (2009), 163-198.
  • 8. Chyzhykov I., Semochko N.: Fast growing entire solutions of linear differential equations. Math. Bull. Shevchenko Sci. Soc. 13 (2016), 1-16.
  • 9. Gundersen G.G.: Finite order solutions of second order linear differential equations. Trans. Amer. Math. Soc. 305 (1988), no. 1, 415-429.
  • 10. Gao S.A., Chen Z.X., Chen T.W.: The Complex Oscillation Theory of Linear Differential Equations. Huazhong Univ. Sci. Tech. Press, Wuhan 1998 (in Chinese).
  • 11. Hayman W.K.: Meromorphic Functions. Oxford Mathematical Monographs, Clarendon Press, Oxford 1964.
  • 12. Hayman W.K.: The local growth of power series: a survey of the Wiman-Valiron method. Canad. Math. Bull. 17 (1974), no. 3, 317-358.
  • 13. He Y.Z., Xiao X.Z.: Algebroid Functions and Ordinary Differential Equations. Science Press, Beijing 1988 (in Chinese).
  • 14. Juneja O.P., Kapoor G.P., Bajpai S.K.: On the (p, q)-order and lower (p, q)-order of an entire function. J. Reine Angew. Math. 282 (1976), 53-67.
  • 15. Juneja O.P., Kapoor G.P., Bajpai S.K.: On the (p, q)-type and lower (p, q)-type of an entire function. J. Reine Angew. Math. 290 (1977), 180-190.
  • 16. Jank G., Volkmann L.: Einführung in die Theorie der ganzen und meromorphen Funktionen mit Anwendungen auf Differentialgleichungen. Birkhäuser Verlag, Basel 1985.
  • 17. Kinnunen L.: Linear differential equations with solutions of finite iterated order. Southeast Asian Bull. Math. 22 (1998), no. 4, 385-405.
  • 18. Laine I.: Nevanlinna theory and complex differential equations. De Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin 1993.
  • 19. Mulyava O.M., Sheremeta M.M., Trukhan, Yu.S.: Properties of solutions of a heterogeneous differential equation of the second order. Carpathian Math.Publ. 11 (2019), no. 2, 379-398.
  • 20. Nevanlinna, R.: Zur Theorie der Meromorphen Funktionen. Acta Math. 46 (1925), no. 1-2, 1-99.
  • 21. Shen X., Tu J., Xu H.Y.: Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q]-ϕ order. Adv. Difference Equ. 2014, 2014:200, 14 pp.
  • 22. Sheremeta M.N.: Connection between the growth of the maximum of the modulus of an entire function and the moduli of the coefficients of its power series expansion, Izv. Vyssh. Uchebn. Zaved. Mat. 2 (1967), 100-108 (in Russian).
  • 23. Sato D.: On the rate of growth of entire functions of fast growth. Bull. Amer.Math. Soc. 69 (1963), 411-414.
  • 24. Singh A.P., Baloria M.S.: On the maximum modulus and maximum term of composition of entire functions. Indian J. Pure Appl. Math. 22 (1991), 1019-1026.
  • 25. Xu H.Y., Tu J.: Oscillation of meromorphic solutions to linear differential equations with coefficients of [p, q]-order. Electron. J. Differential Equations 2014, No. 73, 14 pp.
  • 26. Yang L.: Value Distribution Theory and Its New Research. Science Press, Beijing 1982 (in Chinese).
  • 27. Yang L.: Value Distribution Theory. Springer-Verlag, Berlin 1993.
  • 28. Yang C.C., Yi H.X.: Uniqueness theory of meromorphic functions. Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
Typ dokumentu
Bibliografia
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