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Keywords:
nonlinear differential equation; differential polynomial; Nevanlinna's value distribution theory
nonlinear differential equation; differential polynomial; Nevanlinna's value distribution theory
Summary:
The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation $$ f^{n}(z)+P_{d}(z,f)=p_{1}(z){\rm e}^{\alpha _{1}(z)}+p_{2}(z){\rm e}^{\alpha _{2}(z)}, $$ where $P_d(z,f)$ is a difference-differential polynomial in $f(z)$ of degree $d\leq n-1$ with small functions of $f(z)$ as its coefficients, $p_1$, $p_2$ are nonzero rational functions and $\alpha _1$, $\alpha _2$ are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.
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