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On meromorphic solutions of the Riccati differential equations

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Zhang R., Chen Z.

Annales Polonici Mathematici

2010

tom 99

nr 3

247-262

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Chen Z.

1 Zhang R.

1 2010

Wyniki wyszukiwania

On meromorphic solutions of the Riccati differential equations