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We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation
w' = a(z) + b(z)w + w²,
where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we show that w(z) has at most one Borel exceptional value. Furthermore, we construct numerous examples to illustrate our results.
w' = a(z) + b(z)w + w²,
where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we show that w(z) has at most one Borel exceptional value. Furthermore, we construct numerous examples to illustrate our results.
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Tom
Numer
Strony
247-262
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- School of Mathematical Sciences, South China Normal University, 510631 Guangzhou, People's Republic of China
autor
- School of Mathematical Sciences, South China Normal University, 510631 Guangzhou, People's Republic of China
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-3-3