ON MEROMORPHIC SOLUTIONS OFNONLINEAR COMPLEX DIFFERENTIALEQUATIONS

By utilizing Nevanlinna theory of meromorphic functions, wecharacterize meromorphic solutions of the following nonlinear differential equationof the formf(n)f +P(z,f,f',...,f(t))=P1ea1z+P2ea2z+...+Pme(amz),where n=3, t=0 and m=1 are integers, n=m, P(z,f,f', ...,f(t)) is a differential polynomial in f(z) of degreed =n with small functions off (z) as its coefficients, and a(j), P-j (j=1,2,...,m) are nonzero constants such that|a1|>|a2|>...>|am|. Also we provide the concrete forms of the solutions ofthe equation above, and present some examples illustrating the sharpness of ourresults.

Automated summary

By utilizing Nevanlinna theory of meromorphic functions, this paper characterizes the meromorphic solutions of a specific class of nonlinear differential equations. The concrete forms of the solutions are provided, and examples are presented to illustrate the significance of the results.