no code implementations • 4 Feb 2021 • Nan Li, Jiachuan Geng, Lianzhong Yang
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 $q, u\not\equiv0$.
Complex Variables Primary 30D35, Secondary 39B32
