Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations

DOI10.1007/s00030-016-0427-5zbMath1366.34057OpenAlexW2566167565MaRDI QIDQ523545

Andrea Sfecci, Alessandro Calamai

Publication date: 21 April 2017

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-016-0427-5

zbMATH Keywords

periodic solutionsmultiplicity resultsPoincaré-Birkhoff theoremasymmetric nonlinearitiessystems of ODE's

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Applications of operator theory to differential and integral equations (47N20)

Related Items (9)

Periodic solutions of weakly coupled superlinear systems with indefinite terms ⋮ Odd periodic solutions of fully second-order ordinary differential equations with superlinear nonlinearities ⋮ Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth ⋮ Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities ⋮ An extension of the Poincaré-Birkhoff theorem coupling twist with lower and upper solutions ⋮ Coupling linearity and twist: an extension of the Poincaré-Birkhoff theorem for Hamiltonian systems ⋮ A new fixed point theorem and periodic solutions of nonconservative weakly coupled systems ⋮ Periodic solutions of planar Hamiltonian systems with asymmetric nonlinearities ⋮ Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

Cites Work

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• An avoiding cones condition for the Poincaré-Birkhoff theorem
• On a singular periodic Ambrosetti-Prodi problem
• Periodic perturbations of Hamiltonian systems
• A higher dimensional Poincaré-Birkhoff theorem for Hamiltonian flows
• Multiple periodic solutions of Hamiltonian systems confined in a box
• Multiple periodic solutions of Hamiltonian systems in the plane
• A general method for the existence of periodic solutions of differential systems in the plane
• Half-eigenvalues of periodic Sturm--Liouville problems
• Periodic solutions of weakly coupled superlinear systems
• Planar differential systems at resonance
• Multiple periodic solutions of scalar second order differential equations
• Large scale oscillatory behaviour in loaded asymmetric systems
• On the number of \(2\pi\)-periodic solutions for \(u+g(u)=s(1+h(t))\) using the Poincaré-Birkhoff theorem
• Critical point theory and Hamiltonian systems
• Coincidence degree, and nonlinear differential equations
• Multiple periodic solutions of second order equations with asymmetric nonlinearities
• A higher-dimensional Poincaré-Birkhoff theorem without monotone twist
• Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces.
• A regular perturbation technique for non-linearly coupled oscillators in resonance
• Boundary value problems with jumping nonlinearities
• Boundary-value problems for weakly nonlinear ordinary differential equations
• Periodic Solutions of a System of Coupled Oscillators Near Resonance
• Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities
• Variational Methods
• Resonance and nonlinearity: A survey
• Nonlinear Integral Equations of the Hammerstein Type

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