Non-resonance and double resonance for a planar system via rotation numbers
type: Item
instance of: scholarly article
title: Non-resonance and double resonance for a planar system via rotation numbers
zbMATH Open document ID: 1472.34079
author: Chunlian Liu
author: Pedro J. Torres
author: Dingbian Qian
published in: Results in Mathematics
publication date: 2021-07-07T00:00:00Z
review text: The authors consider a general planar periodic system and propose two existence results. In the first one they compare the nonlinearity with two positively homogeneous functions with ``rotation numbers'' larger than some \(n\) and smaller than \(n+1\). They thus prove that the system has a periodic solution, by the use of the Poincaré-Bohl fixed point theorem. This is a generalization of some classical ``nonresonance'' results. In the second one the above two functions have rotation numbers exactly equal to \(n\) and \(n+1\). Then, in order to avoid possible resonance phenomena, they add two Landesman-Lazer conditions, and they prove again the existence of a periodic solution. The proofs involve delicate analysis in the phase-plane, in order to precisely estimate the rotational properties of the solutions.
reviewed by: Alessandro Fonda
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7369324
zbMATH Keywords: periodic solution
zbMATH Keywords: resonance
zbMATH Keywords: Landesman-Lazer condition
zbMATH Keywords: rotation number
zbMATH Keywords: Poincaré-Bohl theorem
MaRDI profile type: Publication
full work available at URL: s00025-021-01401-w
OpenAlex ID: W3153388811
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DOI: 10.1007/S00025-021-01401-W
description: scientific article; zbMATH DE number 7369324