Finite and infinite order of growth of solutions to linear differential equations near a singular point
Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 315-332
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In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.
In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.
DOI : 10.21136/MB.2020.0148-19
Classification : 30D35, 34M10
Keywords: linear differential equation; growth of solution; finite singular point
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Cherief, Samir; Hamouda, Saada. Finite and infinite order of growth of solutions to linear differential equations near a singular point. Mathematica Bohemica, Tome 146 (2021) no. 3, pp. 315-332. doi: 10.21136/MB.2020.0148-19

[1] Bieberbach, L.: Theorie der gewöhnlichen Differentialgleichungen auf funktionentheoretischer Grundlage dargestellt. Die Grundlehren der Mathematischen Wissenschaften 66. Springer, Berlin (1965), German. | MR | JFM

[2] Fettouch, H., Hamouda, S.: Growth of local solutions to linear differential equations around an isolated essential singularity. Electron. J. Differ. Equ. 2016 (2016), Paper No. 226, 10 pages. | MR | JFM

[3] Hamouda, S.: Finite and infinite order solutions of a class of higher order linear differential equations. Aust. J. Math. Anal. Appl. 9 (2012), Article No. 10, 9 pages. | MR | JFM

[4] Hamouda, S.: Properties of solutions to linear differential equations with analytic coefficients in the unit disc. Electron. J. Differ. Equ. 2012 (2012), Paper No. 177, 8 pages. | MR | JFM

[5] Hamouda, S.: Iterated order of solutions of linear differential equations in the unit disc. Comput. Methods Funct. Theory 13 (2013), 545-555. | DOI | MR | JFM

[6] Hamouda, S.: The possible orders of growth of solutions to certain linear differential equations near a singular point. J. Math. Anal. Appl. 458 (2018), 992-1008. | DOI | MR | JFM

[7] Hayman, W. K.: Meromorphic Functions. Oxford Mathematical Monographs. Clarendon Press, Oxford (1964). | MR | JFM

[8] Khrystiyanyn, A. Ya., Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli. I. Mat. Stud. 23 (2005), 19-30. | MR | JFM

[9] Kinnunen, L.: Linear differential equations with solutions of finite iterated order. Southeast Asian Bull. Math. 22 (1998), 385-405. | MR | JFM

[10] Kondratyuk, A., Laine, I.: Meromorphic functions in multiply connected domains. Fourier Series Methods in Complex Analysis I. Laine University of Joensuu 10. Department of Mathematics, University of Joensuu, Joensuu (2006), 9-111. | MR | JFM

[11] Korhonen, R.: Nevanlinna theory in an annulus. Value Distribution Theory and Related Topics Advances in Complex Analysis and Its Applications 3. Kluwer Academic Publishers, Boston (2004), 167-179. | DOI | MR | JFM

[12] Laine, I.: Nevanlinna Theory and Complex Differential Equations. De Gruyter Studies in Mathematics 15. W. de Gruyter, Berlin (1993). | DOI | MR | JFM

[13] Laine, I., Yang, R.: Finite order solutions of complex linear differential equations. Electron. J. Differ. Equ. 2004 (2004), Paper No. 65, 8 pages. | MR | JFM

[14] Lund, M. E., Ye, Z.: Logarithmic derivatives in annuli. J. Math. Anal. Appl. 356 (2009), 441-452. | DOI | MR | JFM

[15] Tsuji, M.: Potential Theory in Modern Function Theory. Chelsea Publishing Company, New York (1975). | MR | JFM

[16] Whittaker, J. M.: The order of the derivative of a meromorphic function. J. Lond. Math. Soc. 11 (1936), 82-87. | DOI | MR | JFM

[17] Yang, L.: Value Distribution Theory. Springer, Berlin (1993). | DOI | MR | JFM

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