Existence of at most two limit cycles for some non-autonomous differential equations
It is know that the non-autonomous differential equations dx/dt = a(t)+b(t)|x|, where a(t) and b(t) are 1-periodic maps of class C1, have no upper bound for their number of limit cycles (isolated solutions satisfying x(0) = x(1)). We prove that if either a(t) or b(t) does not change sign, then their...
| Authors: | ; |
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| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2023 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/536856 |
| Online Access: | http://hdl.handle.net/2072/536856 |
| Access Level: | Open access |
| Keyword: | limit cycle Non-autonomous differential equation periodic orbit |
| Summary: | It is know that the non-autonomous differential equations dx/dt = a(t)+b(t)|x|, where a(t) and b(t) are 1-periodic maps of class C1, have no upper bound for their number of limit cycles (isolated solutions satisfying x(0) = x(1)). We prove that if either a(t) or b(t) does not change sign, then their maximum number of limit cycles is two, taking into account their multiplicities, and that this upper bound is sharp. We also study all possible configurations of limit cycles. Our result is similar to other ones known for Abel type periodic differential equations although the proofs are quite different. © 2023 American Institute of Mathematical Sciences. All rights reserved. |
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