Unbounded solutions to systems of differential equations at resonance

DOI10.1007/s10884-020-09890-zzbMath1495.34056arXiv2007.00546OpenAlexW3102000066MaRDI QIDQ2116461

Alberto Boscaggin, Walter Dambrosio, Duccio Papini

Publication date: 17 March 2022

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00546

zbMATH Keywords

Lyapunov functionresonanceunbounded solutionssystems of ODEs

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Growth and boundedness of solutions to ordinary differential equations (34C11)

Cites Work

• Unnamed Item
• A higher dimensional Poincaré-Birkhoff theorem for Hamiltonian flows
• Periodic, quasi-periodic and unbounded solutions of radially symmetric systems with repulsive singularities at resonance
• Periodic solutions of second-order differential equations in Hilbert spaces
• Periodic solutions of weakly coupled superlinear systems
• On a generalization of Lazer-Leach conditions for a system of second order ODE's
• Roots of unity and unbounded motions of an asymmetric oscillator
• A note on the existence of unbounded solutions to a perturbed asymmetric oscillator
• Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces.
• Unbounded solutions and periodic solutions of perturbed isochronous Hamiltonian systems at resonance
• A new fixed point theorem and periodic solutions of nonconservative weakly coupled systems
• Bounded and unbounded motions in asymmetric oscillators at resonance
• Bounded perturbations of forced harmonic oscillators at resonance
• Monotone twist maps and periodic solutions of systems of Duffing type
• Unbounded solutions of semilinear equations at resonance
• Oscillations of a forced asymmetric oscillator at resonance
• Unbounded solutions of asymmetric oscillator
• Resonance and nonlinearity: A survey
• Coexistence of unbounded and periodic solutions to perturbed damped isochronous oscillators at resonance
• Unbounded Motions of Perturbed Isochronous Hamiltonian Systems at Resonance
• Resonance in undamped second-order nonlinear equations with periodic forcing
• An infinite-dimensional version of the Poincaré-Birkhoff theorem on the Hilbert cube
• Boundedness and unboundedness of solutions for reversible oscillators at resonance