On the Polynomial Solutions and Limit Cycles of Some Generalized Polynomial Ordinary Differential Equations

Claudia Valls
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Claudia Valls: Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal

Mathematics, 2020, vol. 8, issue 7, 1-11

Abstract: 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.

Keywords: polynomial ordinary differential equations; polynomial solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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