Open Access
·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X
Powered by:
The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to:
Random dynamical systems
Geometry and physics
Dynamical systems with hyperbolic behaviour
Real and complex geometry
Ergodic theory
Distance geometry
Topological dynamics
Global differential geometry
Infinite-dimensional Hamiltonian systems
Symplectic geometry, contact geometry
The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.
Issues up to 2022 co-published with and available at:
Meromorphic solutions to linear differential equations with entire coefficients of [p,q]-order
*Mansouria SaidaniCorresponding authorsaidaniman@yahoo.frDepartment of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227Mostaganem, AlgeriaView full profile →
, Benharrat Belaïdibenharrat.belaidi@univ-mosta.dzDepartment of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227Mostaganem, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
In this paper, we investigate the growth and value distribution of meromorphic solutions to higher order homogeneous and nonhomogeneous linear differential equations in which the coefficients are entire functions of finite [p, q]-order. We get the results about [p, q]-order and the [p, q]-convergence exponent of solutions for such equations.
S.Bank, A general theorem concerning the growth of solutions of first-order algebraic differential equations , Compositio Math . 25 ( 1972 ), 61 – 70 . B.Belaïdi, Growth of solutions to linear differential equations with analytic coefficients of, Electron. J. Differential Equations 2011 , No. 156 , 11 pp. B.Belaïdi, Growth and oscillation theory of, J. Math. Anal. 3 ( 2012 ), no. 1 , 1 – 11 . B.Belaïdi, Iterated order of meromorphic solutions of homogeneous and non-homogeneous linear differential equations, Romai J.,v. 11 , No. 1 ( 2015 ), 33 – 46 . B.Belaïdi, Differential polynomials generated by meromorphic solutions of, Rom. J. Math. Comput. Sci. 5 ( 2015 ), no. 1 , 46 – 62 . T.B.Cao, J.F.Xu and Z.X.Chen, On the meromorphic solutions of linear differential equations on the complex plane, J. Math. Anal. Appl. 364 ( 2010 ), no. 1 , 130 – 142 . A.Ferraoun, B.Belaïdi, On the (p,q)-order of solutions of some complex linear differential equations, Communications in Optimization Theory , Vol. 2017 ( 2017 ), Article ID 17, 1 – 23 . A.A.Goldberg, I. V.Ostrovskii, The distribution of values of meromorphic functions, Irdat Nauk, Moscow, 1970 (in Russian), Transl. Math. Monogr., vol. 236, Amer. Math. Soc., Providence RI, 2008 . G.G.Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. ( 2 ) 37 ( 1988 ), no. 1, 88 – 104 . G.G.Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 ( 1988 ), no. 1 , 415 – 429 . K.Hamani, B.Belaïdi, Growth of solutions of complex linear differential equations with entire coefficients of finite iterated order, Acta Univ. Apulensis Math. Inform. No. 27 ( 2011 ), 203 – 216 . W. K.Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press , Oxford1964 . H.Hu, X.M.Zheng, Growth of solutions to linear differential equations with entire coefficients, Electron. J. Differential Equations 2012 , No. 226 , 15 pp. O.P.Juneja, G.P.Kapoor and 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 . L.Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 ( 1998 ), no. 4 , 385 – 405 . I.Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co. , Berlin, 1993 . L. M.Li, T.B.Cao, Solutions for linear differential equations with meromorphic coefficients of [p, q]-order in the plane, Electron. J. Differential Equations 2012 , No. 195 , 15 pp. J.Liu, J.Tu and L. Z.Shi, Linear differential equations with entire coefficients of [p, q]-order in the complex plane, J. Math. Anal. Appl. 372 ( 2010 ), no. 1 , 55 – 67 . J.R.Long, J.Zhu, On hyper-order of solutions of higher order linear differential equations with meromorphic coefficients, Adv. Difference Equ. 2016 , 2016 : 107 , 13 pp. M.Saidani, B.Belaïdi, On the fast growth of solutions to higher order linear differential equations with entire coefficients, Novi Sad J. Math. , Vol. 46 , No. 2 , 2016 , 117 – 133 . J.Tu, T.Long, Oscillation of complex high order linear differential equations with coefficients of finite iterated order, Electron. J. Qual. Theory Differ. Equ. 2009 , No. 66 , 1 – 13 . J.Tu, Z.X.Chen, Growth of solutions of complex differential equations with meromorphic coefficients of finite iterated order, Southeast Asian Bull. Math. 33 ( 2009 ), no. 1 , 153 – 164 . S.Z.Wu, X.M.Zheng, On meromorphic solutions of some linear differential equations with entire coefficients being Fabry gap series, Adv. Difference Equ. 2015 , 2015 : 32 , 13 pp. C.C.Yang, H.X.Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group , Dordrecht, 2003 . L.Yang, Value distribution theory, Springer-Verlag , Berlin, 1993 . M.L.Zhan, X.M.Zheng, Solutions to linear differential equations with some coefficient being lacunary series of (p, q) −order in the complex plane, Ann. Differential Equations 30 ( 2014 ), no. 3 , 364 – 372 .
Views: 10Downloads: 7Citations: 0
Install Journal of Dynamical Systems and Geometric TheoriesFaster access from your home screen