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Growth of meromorphic solutions of finite logarithmic order of linear difference equations

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Języki publikacji
EN
Abstrakty
EN
In this paper, we deal with the growth and the oscillation of solutions of the linear difference equation an (z) f (z + n) + an-1 (z) f (z + n - 1) + ··· + a1 (z) f (z + 1) + a0 (z) f (z) = 0, where an(z), ···, a0(z) are meromorphic functions of finite logarithmic order such that an(z)a0(z) ≠0.
Rocznik
Tom
Strony
5--20
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
  • Department of Mathematics Laboratory of Pure and Applied Mathematics University of Mostaganem (UMAB) B. P. 227 Mostaganem-(Algeria)
Bibliografia
  • [1] Cao T.B., Liu K., Wang J., On the growth of solutions of complex differential equations with entire coefficients of finite logarithmic order, Math. Reports 15(65), 3(2013), 249-269.
  • [2] Chern Peter T.Y., On meromorphic functions with finite logarithmic order, Trans. Amer. Math. Soc., 358(2)(2006), 473-489.
  • [3] Chiang Y.M., Feng S.J., On the Nevanlinna characteristic of /(z + n) and difference equations in the complex plane, Ramanujan J., 16(1)(2008), 105-129.
  • [4] Halburd R.G., Korhonen R.J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 314(2)(2006), 477-487.
  • [5] Halburd R.G., Korhonen R.J., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31(2)(2006), 463-478.
  • [6] Hayman W.K., Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964.
  • [7] Heittokangas J., Wen Z.T., Functions of finite logarithmic order in the unit disc, Part I. J. Math. Anal. Appl., 415(1)(2014), 435-461.
  • [8] Heittokangas J., Wen Z.T., Functions of finite logarithmic order in the unit disc, Part II. Comput. Methods Funct. Theory, 2014, DOI 10.1007/s40315-014-0089-4.
  • [9] Laine I., Yang C.C., Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2), 76(3)(2007), 556-566.
  • [10] Latreuch Z., Belaïdi B., Growth and oscillation of meromorphic solutions of linear difference equations, Mat. Vernik, 66(2)(2014), 213-222.
  • [11] Wen Z.T., Finite logarithmic order solutions of linear q-difference equations, Bull. Korean Math. Soc., 51(1)(2014), 83-98.
  • [12] Yang C.C., Yi H.X., Uniqueness Theory of Meromorphic Functions, Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-13d057a1-dee3-4c24-82b1-d017ae23bd6c
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