Fast Growing Solutions to Linear Differential Equations with Entire Coefficients Having the Same ρφ-order

Abstract (pdf)

Full text (pdf)

1. A.I. Bandura, O.B. Skaskiv, P.V. Filevych, Properties of entire solutions of some linear PDE's, J. Appl. Math. Comput. Mech. 16 (2) (2017) 17-28.
2. B. Belaïdi, Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order, Electron. J. Differential Equations 70 (2009) 1-10.
3. B. Belaïdi, Growth of solutions to linear equations with analytic coefficients of [p,q]-order in the unit disc, Electron. J. Diff. Equ. 156 (2011) 1-11.
4. B. Belaïdi, On the [p,q]-order of meromorphic solutions of linear differential equations, Acta Univ. M. Belii Ser. Math. (2015) 37-49.
5. B. Belaïdi, Differential polynomials generated by meromorphic solutions of [p,q]-order to complex linear differential equations, Rom. J. Math. Comput. Sci. 5 (1) (2015) 46-62.
6. B. Belaïdi, Growth of ρφ -order solutions of linear differential equations with entire coefficients, PanAmer. Math. J. 27 (4) (2017) 26-42.
7. L.G. Bernal, On growth k-order of solutions of a complex homogeneous linear differential equation, Proc. Amer. Math. Soc. 101 (2) (1987) 317-322.
8. T.B. Cao, Z.X. Chen, X.M. Zheng, J. Tu, On the iterated order of meromorphic solutions of higher order linear differential equations, Ann. Differential Equations 21 (2) (2005) 111-122.
9. T.B. Cao, J.F. Xu, Z.X. Chen, On the meromorphic solutions of linear differential equations on the complex plane, J. Math. Anal. Appl. 364 (1) (2010) 130-142.
10. I. Chyzhykov, N. Semochko, Fast growing entire solutions of linear differential equations, Math. Bull. Shevchenko Sci. Soc. 13 (2016) 1-16.
11. G.G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. (2) 37 (1) (1988) 88-104.
12. W.K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs Clarendon Press, Oxford, 1964.
13. H. Hu, X.M. Zheng, Growth of solutions of linear differential equations with meromorphic coefficients of [p,q]-order, Math. Commun. 19 (2014) 29-42.
14. J. Jank, L. Volkmann, Einführung in die Theorie der Ganzen und Meromorphen Funktionen mit Anwendungen auf Differentialgleichungen. Birkhäuser Verlag, Basel, 1985.
15. O.P. Juneja, G.P. Kapoor, 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.
16. O.P. Juneja, G.P. Kapoor, 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.
17. L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (4) (1998) 385-405.
18. I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin, 1993.
19. L.M. Li, T.B. Cao, Solutions for linear differential equations with meromorphic coefficients of [p,q]-order in the plane, Electron. J. Diff. Equ. 2012 (195) (2012) 1-15.
20. J. Liu, J. Tu, L.Z. Shi, Linear differential equations with entire coefficients of [p,q]-order in the complex plane, J. Math. Anal. Appl. 372 (2010) 55-67.
21. N.S. Semochko, On solutions of linear differential equations of arbitrary fast growth in the unit disc, Mat. Stud. 45 (1) (2016) 3-11.
22. M.N. Sheremeta, 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. J. Tu, H.X. Huang, Complex oscillation of linear differential equations with analytic coefficients of [p,q]-order in the unit disc, Comput. Methods Funct. Theory 15 (2) (2015) 225-246.
24. C.C. Yang, H.X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
25. M.A. Zemirni, B. Belaïdi, On the growth of solutions of higher order complex differential equations with finite [p,q]-order, Theory Appl. Math. Comput. Sci. 7 (1) (2017) 14-26.