TARU PUBLICATIONS
Journal of Dynamical Systems and Geometric Theories cover
Open Access Β·Peer-reviewedΒ·ISSN (Online): 2169-0057Β·ISSN (Print): 1726-037X
Powered by: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:Taylor & Francis
info@tarupublications.com
Open Access Research Article

Hyper-order of solutions to a class of nonlinear complex differential equations

* , ,

* Corresponding author · click or hover a name for details

pp. 31–44Vol. 23Issue 1 & 2November 2025DOI: 10.47974/JDSGT-2024-002XML
Received:
06 Feb 2024
Published Online:
01 Nov 2025
Article type:
Research Article
Language:
EN
Article no.:
JDSGT-2024-002
Pages:
31–44

Abstract

This study focuses on analyzing the hyper-order associated with meromorphic solutions of nonlinear complex differential equations represented by 𝒫[π’ˆ] – Qπ’ˆΞ³π’« = R, where 𝒫[π’ˆ] denotes a differential polynomial in π’ˆ, γ𝒫 indicates for the degree of 𝒫[π’ˆ], and the coefficients of 𝒫[π’ˆ], along with Q = Q(z) and R = R(z), satisfy certain prescribed growth conditions.Β 

Keywords

Subject Classifications

34M0334M0434M0530D2030D35

References

[1] M. Biswas and D. K. Mandal, β€œ On the growth of infinite order solutions of non-linear differential equations with entire coefficients,” Bull. Calcutta Math. Soc., vol. 112, no. 6, pp. 525-538 (2020).[2] M. Biswas and D. C. Pramanik, β€œ Uniqueness of entire function and its linear differential polynomial,” Serdica Math. J., vol. 50, pp. 173-182 (2024).[3] Z. X. Chen and C. C. Yang, β€œ Some further results on the zeros and growths of entire solutions of second order linear differential equations,” Kodai Math. J., vol. 22, pp. 273-285 (1999).[4] W. Cherry and Z. Ye, Nevanlinna’s Theory of Value Distribution. Berlin, Germany: Springer-Verlag (2001).[5] G. Gundersen, β€œ Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates,” J. London Math. Soc., vol. 37, no. 2, pp. 88-104 (1998).[6] W. K. Hayman, Meromorphic Functions. Oxford, U.K.: Clarendon Press (1964).[7] W. K. Hayman, β€œ The local growth of power series: a survey of the Wiman-Valiron method,” Can. Math. Bull., vol. 17, pp. 317-358 (1974).[8] Y. Z. He and X. Z. Xiao, Algebroid Functions and Ordinary Differential Equations. Beijing, China: Science Press (1988).[9] K. H. Kwon, β€œ On the growth of entire functions satisfying second order linear differential equations,” Bull. Korean Math. Soc., vol. 33, no. 3, pp. 487-496 (1996).[10] I. Laine, Nevanlinna Theory and Complex Differential Equations. Berlin, Germany: Walter de Gruyter (1993).[11] Z. Q. Mao, β€œ Uniqueness theorems on entire functions and their linear differential polynomials,” Results Math., vol. 55, pp. 447-456 (2009).[12] D. C. Pramanik and M. Biswas, β€œ On solutions of some non-linear complex differential equations in connection to BrΓΌck conjecture,” Tamkang J. Math., vol. 48, no. 4, pp. 365-375 (2017).[13] D. C. Pramanik, M. Biswas, and R. Mandal, β€œ On the study of BrΓΌck conjecture and some non-linear complex differential equations,” Arab J. Math. Sci., vol. 23, pp. 196-204 (2017).[14] D. C. Pramanik and M. Biswas, β€œ Growth of entire solutions of non-linear differential equations,” Appl. Math. E-Notes, vol. 23, pp. 203-208 (2023).[15] D. C. Pramanik and M. Biswas, β€œ Growth of solutions of non-homogeneous linear differential equations and its applications,” Korean J. Math., vol. 29, no. 1, pp. 65-73 (2021).[16] G. Valiron, Lectures on the General Theory of Integral Functions. New York, USA: Chelsea (1949).[17] L. Yang, Value Distribution Theory. Berlin, Germany: Springer-Verlag (1993).[18] L. Z. Yang, β€œ The growth of linear differential equations and their applications,” Israel J. Math., vol. 147, pp. 359-370 (2005).[19] H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions. Beijing, China: Science Press (1995).Β 
Views: 105Downloads: 11Citations: 0