In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms:
$ \begin{eqnarray*} f^{2}(z)+\widetilde{\omega} f(z)f'(z)+q(z)e^{Q(z)}f(z+c) = u(z)e^{v(z)}, \end{eqnarray*} $
and
$ \begin{eqnarray*} 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, \end{eqnarray*} $
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.
Citation: Nan Li, Jiachuan Geng, Lianzhong Yang. Some results on transcendental entire solutions to certain nonlinear differential-difference equations[J]. AIMS Mathematics, 2021, 6(8): 8107-8126. doi: 10.3934/math.2021470
In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms:
$ \begin{eqnarray*} f^{2}(z)+\widetilde{\omega} f(z)f'(z)+q(z)e^{Q(z)}f(z+c) = u(z)e^{v(z)}, \end{eqnarray*} $
and
$ \begin{eqnarray*} 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, \end{eqnarray*} $
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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Nan Li, Jiachuan Geng, Lianzhong Yang. Some results on transcendental entire solutions to certain nonlinear differential-difference equations[J]. AIMS Mathematics, 2021, 6(8): 8107-8126. doi: 10.3934/math.2021470
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