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- Title
On Meromorphic Solutions of Nonlinear Complex Difference Equations.
- Authors
Zhu, Min; Chen, Jun-Fan
- Abstract
In this paper, we study meromorphic solutions of the following nonlinear complex difference equation f n (z) + P (z) Δ η l f (z) = H 0 (z) + H 1 (z) e p 1 (z) + ⋯ + H m (z) e p m (z) , where n, l, m, q are positive integers with n ≥ 2 , η is a nonzero complex number satisfying Δ η l f (z) ≢ 0 , p 1 , ... , p m are polynomials of degree q, whose leading coefficients α 1 , ... , α m are distinct nonzero complex numbers, and P , H 0 , H 1 , ... , H m are meromorphic functions of order less than q such that P H 1 ... H m ≢ 0. In addition, we analyze meromorphic solutions of the above equation for n = 1 . Our proofs depend on Cartan's theorem and the variation of Nevanlinna's theorem regarding a set of meromorphic functions. Several examples are provided to demonstrate our results. These results generalize some very recent known results.
- Subjects
NONLINEAR difference equations; MEROMORPHIC functions; COMPLEX numbers; SET functions; DIFFERENCE equations; NEVANLINNA theory
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2023, Vol 46, Issue 6, p1
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-023-01574-3