Some results on transcendental entire solutions of certain nonlinear differential-difference equations
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.
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Complex Variables
Primary 30D35, Secondary 39B32
