Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Some results on transcendental entire solutions of certain nonlinear differential-difference equations (2102.02508v1)

Published 4 Feb 2021 in math.CV

Abstract: In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: $f{2}(z)+\widetilde{\omega} f(z)f'(z)+q(z)e{Q(z)}f(z+c)=u(z)e{v(z)}$, and $f{n}(z)+\omega f{n-1}(z)f'(z)+q(z)e{Q(z)}f(z+c)=p_{1}e{\lambda_{1} z}+p_{2}e{\lambda_{2} z}, \quad n\geq 3,$ where $\omega$ is a constant, $\widetilde{\omega}, c, \lambda_{1}, \lambda_{2}, p_{1}, p_{2}$ are non-zero constants, $q, Q, u, v$ are polynomials such that $Q,v$ are not constants and $q,u\not\equiv0$. Our results are improvements and complements of some previous results.

Summary

We haven't generated a summary for this paper yet.