On the Polynomial Solutions and Limit Cycles of Some Generalized Polynomial Ordinary Differential Equations
Keyword(s):
We study equations of the form y d y / d x = P ( x , y ) where P ( x , y ) ∈ R [ x , y ] with degree n in the y-variable. We prove that this ordinary differential equation has at most n polynomial solutions (not necessarily constant but coprime among each other) and this bound is sharp. We also consider polynomial limit cycles and their multiplicity.
1977 ◽
Vol 79
(1-2)
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pp. 79-85
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2014 ◽
Vol 687-691
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pp. 601-605
1984 ◽
Vol 36
(2)
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pp. 176-186
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2003 ◽
Vol 13
(05)
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pp. 1287-1298
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