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On Solutions of Certain Non-Linear Differential-Difference Equations

Complex Variables 2023-05-22 v1

Abstract

We study about solutions of certain kind of non-linear differential difference equations fn(z)+wfn1(z)f(z)+f(k)(z+c)=p1eα1z+p2eα2zf^{n}(z)+wf^{n-1}(z)f^{'}(z)+f^{(k)}(z+c)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z} and fn(z)+wfn1(z)f(z)+q(z)eQ(z)f(z+c)=p1eα1z+p2eα2z,f^{n}(z)+wf^{n-1}(z)f^{'}(z)+q(z)e^{Q(z)}f(z+c)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2} z}, where n2n\geq 2, k0k\geq0 are integers, w,p1,p2,α1w, p_{1}, p_{2}, \alpha_{1} &\& α2\alpha_{2} are non-zero constants satisfying α1\alpha_{1} \neq α2\alpha_{2}, 0≢q0\not\equiv q is a polynomial and QQ is a non-constant polynomial.

Keywords

Cite

@article{arxiv.2305.11234,
  title  = {On Solutions of Certain Non-Linear Differential-Difference Equations},
  author = {Garima Pant and Sanjay Kumar Pant},
  journal= {arXiv preprint arXiv:2305.11234},
  year   = {2023}
}
R2 v1 2026-06-28T10:38:36.507Z