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Abstrakty
In this paper, we shall investigate the existence of finite order entire and meromorphic solutions of linear difference equation of the form fn(z)+p(z)fn-2(z)+L(z, f)=h(z) where L(z, f) is linear difference polynomial in f(z), p(z) is non-zero polynomial and h(z) is a meromorphic function of finite order. We also consider finite order entire solution of linear difference equation of the form fn(z)+p(z)L(z, f)-r(z)eq(z) where r(z) and q(z) are polynomials.
Czasopismo
Rocznik
Tom
Strony
43--59
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Department of Mathematics, Karnatak University, Dharwad-580003, India, renukadyavanal@gmail.com
autor
- Department of Mathematics, Karnatak University, Dharwad-580003, India, madhuramathai@gmail.com
Bibliografia
- [1] Chiang Y.M., Feng S.J., On the Nevanlinna characteristic of f(z +ƞ) and difference equations in the complex plane, Ramanujan J., 16(2008), 105-129.
- [2] Halburd R.G., Korhonen R.J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 34(2006), 477-487.
- [3] Halburd R.G., Korhonen R.J., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31(2006), 463-478.
- [4] Heittokangas J., Korhonen R., Laine I., On meromorphic solutions of certain nonlinear differential equations, Bull. Aust. Math. Soc., 66(2)(2002), 331-343.
- [5] Hayman W.K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
- [6] Laine I., Nevanlinna theory and Complex differential equations, De Gruyter, Berlin, 1993.
- [7] Laine I., Yang C.C., Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2), 76(3)(2007), 556-566.
- [8] Li P., Yang C.C., On the nonexistence of entire solutions of certain type of nonlinear differential equations, J. Math. Anal. Appl., 320(2)(2006), 827-835.
- [9] Qi X., Yang L., Properties of Meromorphic solutions to certain differential-difference equations, Electron. J. Differential Equations, 2013(135)(2013), 1-9.
- [10] Qi X., Dou J., Yang L., The properties of solutions of certain type of difference equations, Adv. Difference Equ., 2014(256)(2014).
- [11] Yang C.C., On entire solutions of a certain type of nonlinear differential equations, Bull. Aust. Math. Soc., 64(2001), 377-380.
- [12] Yang C.C., Laine I., On analogies between nonlinear difference and differential equations, Proc. Japan Acad., 86. Ser. A (2010), 10-14.
- [13] Yang C.C., LI P., On the transcendental solutions of certain type of non-linear differential equations, Arch. Math. (Basel), 82(5)(2004), 442-448.
- [14] Yang C.C., YI H.X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, 2003.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
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Bibliografia
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