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1980•Transactions of the American Mathematical SocietyOpen access

On meromorphic solutions of algebraic differential equations

Sh. Strelitz

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Abstract

The Malmquist Theorem is generalized for equations of the type R ( z , w , w ′ , … , w ( n ) ) = P ( z , w ) / Q ( z , w ) R(z,\,w,\,w’,\, \ldots \,,\,{w^{(n)}})\, = \,{{P(z,\,w)}/{Q(z,\,w)}} where P , Q and R are polynomials of w and w , w ′ , … , w ( n ) w,\,w’,\, \ldots \,,\,{w^{(n)}} respectively with meromorphic coefficients of finite order.

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What this paper is about

The Malmquist Theorem is generalized for equations of the type R ( z , w , w ′ , … , w ( n ) ) = P ( z , w ) / Q ( z , w ) R(z,\,w,\,w’,\, \ldots \,,\,{w^{(n)}})\, = \,{{P(z,\,w)}/{Q(z,\,w)}} where P , Q and R are polynomials of w and w , w ′ , … , w ( n ) w,\,w’,\, \ldots \,,\,{w^{(n)}} respectively with meromorphic coefficients of finite order.

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Available abstract

The Malmquist Theorem is generalized for equations of the type R ( z , w , w ′ , … , w ( n ) ) = P ( z , w ) / Q ( z , w ) R(z,\,w,\,w’,\, \ldots \,,\,{w^{(n)}})\, = \,{{P(z,\,w)}/{Q(z,\,w)}} where P , Q and R are polynomials of w and w , w ′ , … , w ( n ) w,\,w’,\, \ldots \,,\,{w^{(n)}} respectively with meromorphic coefficients of finite order.

Key concepts: Algorithm, Mathematics

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