Multiple periodic solutions for asymptotically linear Duffing equations with resonance

DOI10.1016/j.jmaa.2011.01.049zbMath1227.34040OpenAlexW2051212834MaRDI QIDQ633672

Keqiang Li

Publication date: 29 March 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.01.049

zbMATH Keywords

Morse theoryindex theorymultiple periodic solutionasymptotically linear Duffing equation with resonance

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of operator theory to differential and integral equations (47N20)

Related Items

Multiple periodic solutions for asymptotically linear ordinary differential equations with double resonance ⋮ Nonautonomous nonlinear ODEs: nonresonance conditions and rotation numbers ⋮ Multiple periodic solutions for asymptotically linear Duffing equations with resonance. II. ⋮ On the use of Morse index and rotation numbers for multiplicity results of resonant BVPs

Cites Work

• Unnamed Item
• Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations
• Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems
• Unbounded perturbations of forced second order ordinary differential equations at resonance
• Morse theory and asymptotic linear Hamiltonian system
• Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
• Critical point theory and Hamiltonian systems
• Landesman-Lazer conditions for periodic boundary value problems with asymmetric nonlinearities
• A Maslov-type index theory for symplectic paths
• Infinite dimensional Morse theory and multiple solution problems
• Index theory for symplectic paths with applications
• Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems
• On Poincaré's perturbation theorem and a theorem of W. S. Loud
• The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations