Abstract
We consider the exponential polynomials solutions of non-linear differential-difference equation \({f(z)^{n}+q(z)e^{Q(z)}f^{(k)}(z+c) = P(z)}\), where q(z), Q(z), P(z) are polynomials and n, k are positive integers and the linear differential-difference equation \({f'(z) = f(z + c)}\). Our results show that any exponential polynomials’ solutions of the above two differential-difference equations should have special forms. This paper is a continuation of Wen et al. (Acta Math Sin 28(7):1295–1306, 2012).
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This work was partially supported by the NSFC (No. 11301260), the NSF of Jiangxi (No. 20132BAB211003) and the YFED of Jiangxi (No. GJJ13078) of China. The author also supported by China Scholarship Council (No. 201406825034).
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Liu, K. Exponential Polynomials as Solutions of Differential-Difference Equations of Certain Types. Mediterr. J. Math. 13, 3015–3027 (2016). https://doi.org/10.1007/s00009-015-0669-1
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DOI: https://doi.org/10.1007/s00009-015-0669-1