Subharmonic Solutions of Conservative Systems with Nonconvex Potentials

DOI10.2307/2159584zbMath0752.34027OpenAlexW4250515827MaRDI QIDQ4005747

Alessandro Fonda, Alan C. Lazer

Publication date: 27 September 1992

Full work available at URL: https://doi.org/10.2307/2159584

zbMATH Keywords

critical point theoryconservative systemssubharmonic solutionssystem of second order differential equationsnonconvex potentials\(T\)- periodic solution

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)

Related Items (27)

Existence of periodic solutions for second-order differential equations with singularities and the strong force condition ⋮ Subharmonic oscillations with prescribed minimal period for a class of hamiltonian systems ⋮ Subharmonic solutions of second order nonlinear equations: a time-map approach ⋮ Existence of periodic solutions of sublinear Hamiltonian systems ⋮ Periodic and subharmonic solutions of a class of superquadratic Hamiltonian systems ⋮ Periodic solutions for a kind of second-order neutral differential systems with deviating arguments ⋮ Periodic oscillations for a nonlinear suspension bridge model ⋮ Harmonic and subharmonic solutions of quadratic Liénard type systems with sublinearity ⋮ Oscillatory properties of solutions and nonlinear differential equations with periodic boundary conditions ⋮ Subharmonics for not uniformly coercive Hamiltonian systems ⋮ Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems ⋮ Periodic solutions of a second order nonlinear system ⋮ Periodic solutions for a conservative system of differential equations with a singularity of repulsive type ⋮ Remarks on forced second order Hamiltonian systems with asymmetric potentials ⋮ Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth ⋮ Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments ⋮ Multiple subharmonic solutions in Hamiltonian system with symmetries ⋮ Bounded solutions for a forced bounded oscillator without friction ⋮ Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities ⋮ Subharmonic solutions with prescribed minimal period of a class of nonautonomous Hamiltonian systems ⋮ Subharmonic solutions of sublinear second order systems with impacts ⋮ Subharmonic oscillations of a class of Hamiltonian systems ⋮ Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems ⋮ Periodic solutions for sublinear systems via variational approach ⋮ Subharmonic solutions of a nonconvex noncoercive Hamiltonian system ⋮ Subharmonic solutions in reversible non-autonomous differential equations ⋮ Periodic solutions of a Liénard equation with forcing term

Cites Work

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• Subharmonic oscillations of forced pendulum-type equations
• Nonlinear oscillations and boundary value problems for Hamiltonian systems
• Subharmonic solutions and Morse theory
• Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems
• Critical point theory and Hamiltonian systems
• Periodic solutions of Duffing's equations with superquadratic potential
• Subharmonic solutions for second order differential equations
• A ``Birkhoff-Lewis type result for a class of Hamiltonian systems
• On the periodic motions near a given periodic motion of a dynamical system
• Periodic solutions of x+f(x,t)=0 via the Poincaré-Birkhoff theorem
• Subharmonic oscillations of convex Hamiltonian systems
• Subharmonics for convex nonautonomous hamiltonian systems
• On subharmonic solutions of hamiltonian systems

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