Asymptotic behavior of periodic solutions in one-parameter families of Li\'{e}nard equations
| Autor: | Pedro Toniol Cardin, Douglas D. Novaes |
|---|---|
| Přispěvatelé: | Universidade Estadual Paulista (Unesp), Universidade Estadual de Campinas (UNICAMP) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Oscillation theory
Differential equation 34C07 34C25 34C26 34C29 34D15} Applied Mathematics 010102 general mathematics Mathematical analysis Averaging theory Relaxation oscillation theory 01 natural sciences 010101 applied mathematics Limit cycles Liénard equation Relaxation (approximation) 0101 mathematics Mathematics - Dynamical Systems Link (knot theory) Analysis Mathematics |
| Zdroj: | Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| Popis: | Made available in DSpace on 2020-12-12T00:54:25Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) In this paper, we consider one-parameter ( λ>0) families of Liénard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of λ>0. To prove our main result we use the relaxation oscillation theory and a topological version of the averaging theory. More specifically, the first one is appropriate for studying the periodic solutions for large values of λ and the second one for small values of λ. In particular, our hypotheses allow us to establish a link between these two theories. Universidade Estadual Paulista (UNESP) Faculdade de Engenharia, Ilha Solteira Universidade Estadual de Campinas (UNICAMP) Instituto de Matemática Estatística e Computação Científica Campinas Universidade Estadual Paulista (UNESP) Faculdade de Engenharia, Ilha Solteira FAPESP: 2013/24541-0 FAPESP: 2018/13481-0 FAPESP: 2018/16430-8 FAPESP: 2019/00976-4 FAPESP: 2019/10269-3 CNPq: 306649/2018-7 CNPq: 438975/2018-9 CAPES: 88881.030454/2013-0 |
| Databáze: | OpenAIRE |
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