Some results on transcendental entire solutions of certain nonlinear differential-difference equations

Abstract

In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: $f^2(z)+\tilde{\omega }f(z)f^{\prime }(z)+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}$, and $f^n(z)+\omega f^{n-1}(z)f^{\prime }(z)+q(z)e^{Q(z)}f(z+c)=p_1{e}^{{\lambda }_{1}z}+p_2{e}^{{\lambda }_{2}z},n\ge 3,$ where $\omega$ is a constant, $\tilde{\omega },c,{\lambda }_1,{\lambda }_2,p_1,p_2$ are non-zero constants, $q,Q,u,v$ are polynomials such that $Q,v$ are not constants and $q,u\not\equiv 0$. Our results are improvements and complements of some previous results.

References in corpus (2)

• An extension of Picard's theorem for meromorphic functions of small hyper-order
• Questions on meromorphic functions and complex differential equations