Boundedness in asymmetric oscillations at resonance in a critical situation
type: Item
instance of: scholarly article
title: Boundedness in asymmetric oscillations at resonance in a critical situation
author: Shufang Zhang
author: Xinli Zhang
published in: Taiwanese Journal of Mathematics
publication date: 2022-11-29T00:00:00Z
review text: In this paper, the second-order differential equation \[ x'' + a x^+ - b x^- + \varphi(x) = p(t) \] is considered, where \(x^+=\max\{x,0\}\), \(x^-=\max\{-x,0\}\), \(a\) and \(b\) are positive constants, and \(p\) is periodic. A sufficient condition for every solution to be bounded is established.
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 37E40
zbMATH DE Number: 7624536
zbMATH Keywords: asymmetric oscillations
zbMATH Keywords: at resonance
zbMATH Keywords: boundedness
zbMATH Keywords: critical situation
zbMATH Keywords: twist theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/tjm/220404
OpenAlex ID: W4226000230
cites work: Unbounded solutions of semilinear equations at resonance
cites work: Roots of unity and unbounded motions of an asymmetric oscillator
cites work: On the Dirichlet problem for weakly non-linear elliptic partial differential equations
cites work: Oscillations of a forced asymmetric oscillator at resonance
cites work: Boundedness for the general semilinear Duffing equations via the twist theorem
cites work: Bounded perturbations of forced harmonic oscillators at resonance
cites work: Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
cites work: Boundedness in asymmetric oscillations
cites work: Boundedness in nonlinear oscillations at resonance
cites work: Q3294369
cites work: Asymmetric Oscillators and Twist Mappings
cites work: Invariant tori and boundedness in asymmetric oscillations.
cites work: A new method for the boundedness of semilinear Duffing equations at resonance
cites work: Boundedness of semilinear Duffing equations at resonance in a critical situation
cites work: Quasi-periodic solutions for the general semilinear Duffing equations with asymmetric nonlinearity and oscillating potential
DOI: 10.11650/TJM/220404
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description: scientific article; zbMATH DE number 7624536