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On the comparative growth analysis of solutions of complex linear differential equations with entire and meromorphic coefficients of $\left[ p,q\right] -\varphi $ order | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 175، دوره 13، شماره 2، مهر 2022، صفحه 2175-2183 اصل مقاله (423.54 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22306.2348 | ||
| نویسندگان | ||
| Ravi Agarwal1؛ Sanjib Kumar Datta2؛ Nityagopal Biswas* 3؛ Samten Tamang4، 5 | ||
| 1Department of Mathematics, Texas A & M University - Kingsville, 700 University Blvd., MSC 172, Kingsville, Texas 78363-8202, USA | ||
| 2Department of Mathematics, University of Kalyani, Kalyani, Dist.: Nadia, PIN: 741235, West Bengal, India | ||
| 3Department of Mathematics, Chakdaha College, Chakdaha, Nadia, Pin: 741222, West Bengal, India | ||
| 4Raja Rammohunpur, N.B.U., District-Darjeeling, PIN-734013, West Bengal, India | ||
| 5Formerly:Department of Mathematics, The University of Burdwan, Golapbag, Burdwan, Pin - 713104, West Bengal, India | ||
| تاریخ دریافت: 15 دی 1399، تاریخ بازنگری: 01 بهمن 1399، تاریخ پذیرش: 07 مرداد 1400 | ||
| چکیده | ||
| Let $\varphi $ be a non-decreasing unbounded function and $p,q$ be any two positive integers with $p\geq q\geq 1.$ The relations between the growth of entire or meromorphic coefficients and the growth of entire or meromorphic solutions of general complex linear differential equation with entire or meromorphic coefficients of finite $\left[ p,q\right] $-$\varphi $ order are investigated in this paper. Improving and extending some earlier results of J. Liu, J. Tu, L.Z. Shi, L.M. Li, T.B. Cao and others, we obtain some more results here. | ||
| کلیدواژه‌ها | ||
| Entire function؛ Meromorphic function؛ q]-\varphi $ order؛ $[p؛ q]-\varphi $ exponent of convergence؛ Linear differential equations | ||
| مراجع | ||
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[1] B. Belaidi, On the iterated order and the fixed points of entire solutions of some complex linear differential equations, Electron. J. Qual. Theory Differ. Eqn. 9 (2006), 1–11. [2] N. Biswas and S. Tamang, Growth of solutions to linear differential equations to with entire coefficients of [p, q]- order in the complex plane, Commun. Korean Math. Soc. 33 (2018), no. 4, 1217–1227. [3] B. Bouabdelli and B. Belaidi, Growth and complex oscillation of linear differential equations with meromorphic coefficients of [p, q] − φ order, Int. J. Anal. Appl. 6 (2014), no. 2, 178–194. [4] T.B. Cao, J.F. Xu and Z.X. Chen, On the meromorphic solutions of linear differential equations on complex plane, J. Math. Anal. Appl. 364 (2010), 130–142.[5] S. K. Datta and N. Biswas, Growth properties of solutions of complex linear differential-difference equations with coefficients having the same φ-order, Bull. Cal. Math. Soc. 111 (2019), no. 3, 253–266. [6] S. K. Datta and N. Bisaws, On the growth analysis of meromorphic solutions of finite φ-order of linear difference equations, Anal. 40 (2020), no. 4, 193–202. [7] K. Hamani and B. Belaidi, Iterated order of solutions of linear differential equations with entire coefficients, Electron. J. Qual. Theory Differ. Equ. 32 (2010), 1–17. [8] S. K. Datta and N. Bisaws, On the growth analysis of meromorphic solutions of finite φ-order of linear difference equations, Anal. 40 (2020), no. 4, 193–202. [9] W.K. Hayman, Meromorphic functions, Clarendon press, Oxford, 1964. [10] Y.Z. He and X.Z. Xiao, Algebroid functions and ordinary differential equations, in Chinese, Science Press, Beijing, 1988. [11] I. Laine, Nevanlinna theory and complex differential equations, Walter de Gruyter, Berlin, 1993. [12] L.M. Li and T.B. Cao, Solutions for linear differential equations with meromorphic coefficients of [p, q]−order in the plane, Electron. J. Differ. Equ. 2012 (2012), no. 195, 1–15. [13] 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), 55–67. [14] X. Shen, J. Tu and H.Y. Xu, Complex oscillation of a second-order linear differential equation with entire coe cients of [p, q] − φ order, Adv. Difference Equ. 2014 (2014), Article ID: 200, 1-15. [15] G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949. [16] H.Y. Xu and J. Tu, Oscillation of meromorphic solutions to linear differential equations with coefficients of [p, q] −order, Electron. J. Differ. Equ. 2014 (2014), no. 73, 1–14. | ||
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