Meromorphic solutions to non-linear differential-difference equations
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Date
2018-04-17
Authors
Song, Changjiang
Liu, Kai
Ma, Lei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the non-linear differential-difference equation
c(z)w(z + 1) + α(z) w′(z)/w(z) = R(z, w(z)),
where R(z, w(z)) is rational in w(z) with rational coefficients, α(z) and c(z) are non-zero rational functions. We give necessary conditions on the degree of R(z, w) for the above equation to admit a transcendental meromorphic solution of hyper-order ρ2(w) < 1. We also consider the admissible rational solutions of the above equation.
Description
Keywords
Meromorphic solutions, Differential-difference equations, Hyper-order
Citation
Song, C., Liu, K., & Ma, L. (2018). Meromorphic solutions to non-linear differential-difference equations. <i>Electronic Journal of Differential Equations, 2018</i>(93), pp. 1-12.
Rights
Attribution 4.0 International