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- W3163852016 abstract "<abstract> In this paper, we study rational solutions of the Abel differential equations $ dy/dx = f_m(x)y^2+g_n(x)y^3 $, where $ f_m(x) $ and $ g_n(x) $ are real polynomials of degree $ m $ and $ n $ respectively. The main result of the paper is as follows: We give a systematic upper bound on the number of the nontrivial rational solutions of such equations in all these cases. Then we prove that these upper bounds can be reached in most cases. Finally, we present some examples of Abel equations having exactly $ i $ nontrivial rational solutions, where $ 1leq ileq 5 $. </abstract>" @default.
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- W3163852016 date "2021-01-01" @default.
- W3163852016 modified "2023-10-11" @default.
- W3163852016 title "THE NUMBER OF RATIONAL SOLUTIONS OF ABEL EQUATIONS" @default.
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- W3163852016 doi "https://doi.org/10.11948/20200475" @default.
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