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A remark on meromorphic solutions of differential equations


Author: Sh. Strelitz
Journal: Proc. Amer. Math. Soc. 65 (1977), 255-261
MSC: Primary 34A20
DOI: https://doi.org/10.1090/S0002-9939-1977-0486726-X
MathSciNet review: 0486726
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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 $ \vert z\vert < \infty $, then $ Q(z,w)$ does not depend on w. An example of possible applications is stated.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0486726-X
Keywords: Meromorphic solutions, algebraic differential equations
Article copyright: © Copyright 1977 American Mathematical Society

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