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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON THE ABEL DIFFERENTIAL EQUATIONS OF THIRD KIND

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Author(s):
Oliveira, Regilene [1] ; Valls, Claudia [2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, ICMC, Dept Matemat, Ave Trabalhador Sao Carlense 400, BR-13566590 So Carlos, SP - Brazil
[2] Univ Tecn Lisboa, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon - Portugal
Total Affiliations: 2
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 25, n. 5, p. 1821-1834, MAY 2020.
Web of Science Citations: 0
Abstract

Abel equations of the first and second kind have been widely studied, but one question that never has been addressed for the Abel polynomial differential systems is to understand the behavior of its solutions (without knowing explicitly them), or in other words, to obtain its qualitative behavior. This is a very hard task that grows exponentially as the number of parameters in the equation increases. In this paper, using Poincare compactification we classify the topological phase portraits of a special kind of quadratic differential system, the Abel quadratic equations of third kind. We also describe the maximal number of polynomial solutions that Abel polynomial differential equations can have. (AU)

FAPESP's process: 17/20854-5 - Qualitative theory of ordinary differential equations: integrability, periodic orbits and phase portraits
Grantee:Regilene Delazari dos Santos Oliveira
Support type: Regular Research Grants