Subharmonic bouncing solutions for a class of sublinear impact oscillators with indefinite weight

DOI10.3934/cpaa.2023126OpenAlexW4390118887MaRDI QIDQ6120948

Zhi Guo Wang, Chao Wang, Qihuai Liu

Publication date: 21 February 2024

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2023126

zbMATH Keywords

KAM methodimpact oscillatorsperiodic bouncing solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Cites Work

• Existence of periodic solutions of sublinear Hamiltonian systems
• Existence of quasi-periodic solutions and Littlewood's boundedness problem of sub-linear impact oscillators
• Periodic bouncing solutions for attractive singular second-order equations
• Invariant tori for asymptotically linear impact oscillators
• Impact oscillators of Hill's type with indefinite weight: periodic and chaotic dynamics
• Chaotic, regular and unbounded behaviour in the elastic impact oscillator
• Periodic orbits of a collinear restricted three-body problem
• Non-smooth dynamical systems
• Periodic bouncing solutions for Hill's type sub-linear oscillators with obstacles
• On Littlewood’s boundedness problem for sublinear Duffing equations
• Dual billiards, twist maps and impact oscillators
• Existence of quasiperiodic solutions and Littlewood’s boundedness problem of Duffing equations with subquadratic potentials
• Bouncing solutions of an equation with attractive singularity
• Periodic Motions of Linear Impact Oscillators via the Successor Map
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