Abstract
In this paper, the growth of the meromorphic solutions of the equation
where L, M, N are birational functions, is studied. We have proved that if L(z, f) satisfies a quite general condition, then f must be of finite order. Furthermore, if L(z, f) ≡0, and M(z, f), N(z, f) are polynomials in f, then the order of any entire solution of the equation is a positive integral multiple of \(\frac{1}{2}\). Furthermore, we give a criterion of the normality relating to algebraic differential equations and use it to derive the growth of some solutions of a certain kind of algebraic differential equations.
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Liao, L. (2000). On the Growth of Solutions of Algebraic Differential Equations. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0269-8_38
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DOI: https://doi.org/10.1007/978-1-4613-0269-8_38
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