Properties of higher order differential polynomials generated by solutions of complex differential equations in the unit disc

• Autorzy: Latreuch Z. , Belaidi B.
• Języki publikacji: EN

Abstrakty

EN

The main purpose of this paper is to study the controllability of solutions of the differential equation [...] In fact, we study the growth and oscillation of higher order differential polynomial with meromorphic coefficients in the unit disc [...] generated by solutions of the above kth order differential equation.

Słowa kluczowe

EN

iterated p-order; linear differential equations; polynomials; unit disc

PL

równania różniczkowe; równania różniczkowe liniowe; wielomiany

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2014
• Tom: Vol. 37
• Strony: 67--84
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Latreuch Z.

• Department of Mathematics Laboratory of Pure and Applied Mathematics University of Mostaganem (UMAB) B. P. 227 Mostaganem-(Algeria)

autor

Belaidi B.

• Department of Mathematics Laboratory of Pure and Applied Mathematics University of Mostaganem (UMAB) B. P. 227 Mostaganem-(Algeria)

Bibliografia

• [1] S. Bank, General theorem concerning the growth of solutions of first-order algebraic differential equations, Compositio Math. 25 (1972), 61-70.
• [2] B. Belaidi, Oscillation of fast growing solutions of linear differential equations in the unit disc, Acta Univ. Sapientiae Math. 2 (2010), no. 1, 25–38.
• [3] B. Belaidi, A. El Farissi, Fixed points and iterated order of differential polynomial generated by solutions of linear differential equations in the unit disc, J. Adv. Res. Pure Math. 3 (2011), no. 1, 161–172.
• [4] L. G. Bernal, On growth k-order of solutions of a complex homogeneous linear differential equation, Proc. Amer. Math. Soc. 101 (1987), no. 2, 317–322.
• [5] T. B. Cao and H. X. Yi, The growth of solutions of linear differential equations with coefficients of iterated order in the unit disc, J. Math. Anal. Appl. 319 (2006), no. 1, 278–294.
• [6] T. B. Cao, The growth, oscillation and fixed points of solutions of complex linear differential equations in the unit disc, J. Math. Anal. Appl. 352 (2009), no. 2, 739-748.
• [7] T. B. Cao, H. Y. Xu and C. X. Zhu, On the complex oscillation of differential polynomials generated by meromorphic solutions of differential equations in the unit disc, Proc. Indian Acad. Sci. Math. Sci. 120 (2010), no. 4, 481–493.
• [8] T. B. Cao and Z. S. Deng, Solutions of non-homogeneous linear differential equations in the unit disc, Ann. Polo. Math. 97(2010), no. 1, 51-61.
• [9] T. B. Cao, L. M. Li, J. Tu and H. Y. Xu, Complex oscillation of differential polynomials generated by analytic solutions of differential equations in the unit disc, Math. Commun. 16 (2011), no. 1, 205–214.
• [10] Z. X. Chen and K. H. Shon, The growth of solutions of differential equations with coefficients of small growth in the disc, J. Math. Anal. Appl. 297 (2004), no. 1, 285–304.
• [11] I. E. Chyzhykov, G. G. Gundersen and J. Heittokangas, Linear differential equations and logarithmic derivative estimates, Proc. London Math. Soc. (3) 86 (2003), no. 3, 735–754.
• [12] A. El Farissi, B. Belaidi and Z. Latreuch, Growth and oscillation of differential polynomials in the unit disc, Electron. J. Diff. Equ., Vol. 2010(2010), No. 87, 1-7.
• [13] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford, 1964.
• [14] J. Heittokangas, On complex differential equations in the unit disc, Ann. Acad. Sci. Fenn. Math. Diss. 122 (2000), 1-54.
• [15] J. Heittokangas, R. Korhonen and J. Rattya, Fast growing solutions of linear differential equations in the unit disc, Results Math. 49 (2006), no. 3-4, 265–278.
• [16] J. Heittokangas, R. Korhonen and J. Rattya, Growth estimates for solutions of linear complex differential equations, Ann. Acad. Sci. Fenn. Math. 29 (2004), no. 1, 233–246.
• [17] L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), no. 4, 385-405.
• [18] I. Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, 1993.
• [19] I. Laine and J. Rieppo, Differential polynomials generated by linear differential equations, Complex Var. Theory Appl. 49 (2004), no. 12, 897–911.
• [20] I. Laine, Complex differential equations, Handbook of differential equations: ordinary differential equations. Vol. IV, 269–363, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008.
• [21] Z. Latreuch, B. Belaidi and Abdallah El Farissi, Complex oscillation of differential polynomials in the unit disc, Period. Math. Hungar. 66 (2013), no. 1, 45–60.
• [22] Z. Latreuch and B. Belaidi, Growth and oscillation of differential polynomials generated by complex differential equations, Electron. J. Diff. Equ., Vol. 2013 (2013), No. 16, 1-14.
• [23] Z. Latreuch and B. Belaidi, Properties of solutions of complex differential equations in the unit disc, International Journal of Analysis and Applications, Volume 4, Number 2 (2014), 159-173.
• [24] Z. Latreuch and B. Bela¨ıdi, Further results on the properties of differential polynomials generated by solutions of complex differential equations, Submitted.
• [25] M. Tsuji, Potential Theory in Modern Function Theory, Chelsea, New York, (1975), reprint of the 1959 edition.