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Entire Solutions of Certain Non-Linear Differential-Difference Equations


Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, India
2 Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi, New Delhi-110078, India
     

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We study existence and non-existence of finite order transcendental entire solutions of some non-linear differential-difference equations.

Keywords

Nevanlinna Theory, Entire Functions, Difference Equations, Differential-Difference Equations.
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  • M. F. Chen and N. Cui, On zeros and growth of solutions of complex difference equations, Adv. Difference Equ., 2021(1) (2021), 1–16.
  • M. F. Chen and Z. S. Gao, Entire solutions of certain type of nonlinear differential equations and differential-difference equations, J. Comput. Anal. Appl., 24 (2018), 137–147.
  • W. Chen, P. Hu and Q. Wang, Entire Solutions of Two Certain Types of Non-linear Differential-Difference Equations, Comput. Methods Funct. Theory, 21(2) (2021), 199–218.
  • Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f (z+η) and difference equations in the complex plane, Ramanujan J., 16(1) (2008), 105–129.
  • R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 314 (2006), 477–487.
  • R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 31 (2006), 463–478.
  • R. Halburd, R. Korhonen and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Transa. American Math. Soc., 366(8) (2014), 4267–4298.
  • I. Laine, Nevanlinna Theory and Complex Differential Equations, W. de Gruyter, Berlin, 1993.
  • N. N. Liu, W. L, T. Shen and C. C. Yang, Entire solutions of certain type of difference equations, J. Inequal. Appl., 2014(1) (2014), 1–9.
  • W. L, L. Wu, D. Wang and C. Yang, The existence of solutions to certain type of nonlinear difference-differential equations, Open Math., 16(1) (2018), 806–815.
  • J. Rong and J. Xu, Three Results on the nonlinear differential equations and differential-difference equations, Mathematics, 7(6) (2019), 539.
  • Z. T. Wen, J. Heittokangas and I. Laine, Exponential polynomials as solutions of certain nonlinear difference equations, Acta Math. Sin. (Engl. Ser.), 28(7) (2012), 1295–1306.
  • J. Xu and J. Rong, Entire functions of two classes of nonlinear difference equations, In J. Physics: Conference Series, 1592(1) (2020), 012058.
  • C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Kluwer Academic, Dordrecht, Beijing, 2003.
  • F. Zhang, N. Liu, W. L and C. Yang, Entire solutions of certain class of differential-difference equations, Adv. Difference Equ., 2015(1) (2015), 1–9.

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  • Entire Solutions of Certain Non-Linear Differential-Difference Equations

Abstract Views: 160  |  PDF Views: 1

Authors

Garima Pant
Department of Mathematics, University of Delhi, Delhi-110007, India
Sanjay Kumar Pant
Department of Mathematics, Deen Dayal Upadhyaya College, University of Delhi, New Delhi-110078, India

Abstract


We study existence and non-existence of finite order transcendental entire solutions of some non-linear differential-difference equations.

Keywords


Nevanlinna Theory, Entire Functions, Difference Equations, Differential-Difference Equations.

References





DOI: https://doi.org/10.18311/jims%2F2023%2F31301