A remark on meromorphic solutions of differential equations

Strelitz, Sh.

doi:10.1090/S0002-9939-1977-0486726-X

A remark on meromorphic solutions of differential equations
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Proc. Amer. Math. Soc. 65 (1977), 255-261 Request permission

Abstract:

The following assertion is proven. Suppose the functions F, P, Q of the differential equation $F(z,w,w’,{w^{(n)}}) = P(z,w)/Q(z,w)$ to be polynomials of all their corresponding variables. If the considered equation has a transcendental meromorphic solution in $|z| < \infty$, then $Q(z,w)$ does not depend on w. An example of possible applications is stated.

References

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