Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, Volume 8, Issue 6, pp. 561 - 649

We study the question of the existence of periodic solutions of Hamiltonian systems of the form: q¨+V (t,q)=0whereV=∑1≦i≠j3V (t,q −q )with V(t, ξ) T-periodic...

periodic solution | generalized T-periodic solution | collision | 3-body problem | MATHEMATICS, APPLIED | COLLISION | PERIODIC SOLUTION | 3-BODY PROBLEM | GENERALIZED T-PERIODIC SOLUTION

periodic solution | generalized T-periodic solution | collision | 3-body problem | MATHEMATICS, APPLIED | COLLISION | PERIODIC SOLUTION | 3-BODY PROBLEM | GENERALIZED T-PERIODIC SOLUTION

Journal Article

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Noether’s theorem of Hamiltonian systems with generalized fractional derivative operators

International Journal of Non-Linear Mechanics, ISSN 0020-7462, 12/2018, Volume 107, pp. 34 - 41

In this paper, we present two “transfer formulas” for generalized fractional derivative operators, and derive a Noether type symmetry theorem of fractional...

Noether’s theorem | Hamiltonian systems | Generalized fractional derivatives operator | Calculus of variations

Noether’s theorem | Hamiltonian systems | Generalized fractional derivatives operator | Calculus of variations

Journal Article

3.
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Noether's theorem of Hamiltonian systems with generalized fractional derivative operators

International Journal of Non-Linear Mechanics, ISSN 0020-7462, 12/2018, Volume 107, pp. 34 - 41

In this paper, we present two “transfer formulas” for generalized fractional derivative operators, and derive a Noether type symmetry theorem of fractional...

Hamiltonian systems | Generalized fractional derivatives operator | Calculus of variations | Noether's theorem | MECHANICS | CALCULUS | LINEAR VELOCITIES | FORMULATION | Environmental law

Hamiltonian systems | Generalized fractional derivatives operator | Calculus of variations | Noether's theorem | MECHANICS | CALCULUS | LINEAR VELOCITIES | FORMULATION | Environmental law

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 08/2017, Volume 36, pp. 116 - 138

We deal with the following second-order Hamiltonian systems ü−L(t)u+∇W(t,u)=0, where L∈C(R,RN2) is a symmetric and positive define matrix for all t∈R,...

Ground state | Second-order Hamiltonian system | Generalized Nehari manifold | Homoclinic orbit | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | EQUATIONS | PRINCIPLE | POTENTIALS

Ground state | Second-order Hamiltonian system | Generalized Nehari manifold | Homoclinic orbit | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | EQUATIONS | PRINCIPLE | POTENTIALS

Journal Article

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Homoclinic solutions for singular Hamiltonian systems without the strong force condition

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2019, Volume 472, Issue 1, pp. 352 - 371

We consider the existence of homoclinic orbits at the origin of a Hamiltonian system q¨+V′(q)=0 in RN(N≥3) where V has a strict global maximum at q=0 and a...

Morse theory | Homoclinic solution | Singular Hamiltonian system | Strong-force condition | Minimax methods | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | MULTIPLICITY | NON-COLLISION SOLUTIONS | CRITICAL-POINTS | MATHEMATICS | PRESCRIBED ENERGY | ORBITS | GENERALIZED SOLUTIONS

Morse theory | Homoclinic solution | Singular Hamiltonian system | Strong-force condition | Minimax methods | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | MULTIPLICITY | NON-COLLISION SOLUTIONS | CRITICAL-POINTS | MATHEMATICS | PRESCRIBED ENERGY | ORBITS | GENERALIZED SOLUTIONS

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2019, Volume 2019, Issue 1, pp. 1 - 14

Applying the Generalized Nonsmooth Saddle Point Theorem, we obtain multiple nontrivial periodic bouncing solutions for systems x¨=f(t,x) $\ddot{x}=f(t,x)$ with...

34C25 | Periodic bouncing solution | 70H05 | Mathematics | Generalized Nonsmooth Saddle Point Theorem | 49J35 | 74M20 | Ordinary Differential Equations | 74G35 | Analysis | Multiplicity | Impact Hamiltonian systems | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Hamiltonian functions | Bouncing | Saddle points

34C25 | Periodic bouncing solution | 70H05 | Mathematics | Generalized Nonsmooth Saddle Point Theorem | 49J35 | 74M20 | Ordinary Differential Equations | 74G35 | Analysis | Multiplicity | Impact Hamiltonian systems | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Hamiltonian functions | Bouncing | Saddle points

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2014, Volume 234, pp. 142 - 149

Some existence and multiplicity results are obtained for periodic solutions of nonautonomous second-order discrete Hamiltonian systems with partially periodic...

Discrete Hamiltonian systems | Periodic solutions | Generalized saddle point theorem | (P.S.) condition | Discrete Hamiltonian systems (PS) condition | EXISTENCE | MATHEMATICS, APPLIED | Computation | Mathematical models | Critical point

Discrete Hamiltonian systems | Periodic solutions | Generalized saddle point theorem | (P.S.) condition | Discrete Hamiltonian systems (PS) condition | EXISTENCE | MATHEMATICS, APPLIED | Computation | Mathematical models | Critical point

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 11/2017, Volume 104, pp. 741 - 747

•The Generalized Nonsmooth Saddle Point Theorem is firstly proved.•Different critical point theorem for finding the solution is used.•Periodic bouncing...

Impact | Second order Hamiltonian systems | Periodic bouncing solution | Generalized Nonsmooth Saddle Point Theorem | PERIODIC-SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | Generalized Nonsmooth Saddle Point | Theorem | PHYSICS, MATHEMATICAL

Impact | Second order Hamiltonian systems | Periodic bouncing solution | Generalized Nonsmooth Saddle Point Theorem | PERIODIC-SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | Generalized Nonsmooth Saddle Point | Theorem | PHYSICS, MATHEMATICAL

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 1/2012, Volume 67, Issue 1, pp. 475 - 482

For a generalized Hamiltonian system with the action of small forces of perturbation, the Lie symmetries, symmetrical perturbation, and adiabatic invariants is...

Engineering | Vibration, Dynamical Systems, Control | Generalized Hamiltonian system | Symmetrical perturbation | Adiabatic invariant | Mechanics | Automotive Engineering | Mechanical Engineering | Lie symmetry | Exact invariant | CONSERVED QUANTITIES | MEI SYMMETRY | LIE SYMMETRICAL PERTURBATION | ENGINEERING, MECHANICAL | MECHANICS | CONFORMAL-INVARIANCE | MECHANICAL SYSTEMS | DYNAMICS | CONSTRAINTS | HOJMAN TYPE | Peace movements | Analysis | Adiabatic flow | Mathematical analysis | Lie groups | Transformations | Perturbation | Equations of motion | Hamiltonian functions | Invariants | Nonlinear dynamics | Dynamical systems

Engineering | Vibration, Dynamical Systems, Control | Generalized Hamiltonian system | Symmetrical perturbation | Adiabatic invariant | Mechanics | Automotive Engineering | Mechanical Engineering | Lie symmetry | Exact invariant | CONSERVED QUANTITIES | MEI SYMMETRY | LIE SYMMETRICAL PERTURBATION | ENGINEERING, MECHANICAL | MECHANICS | CONFORMAL-INVARIANCE | MECHANICAL SYSTEMS | DYNAMICS | CONSTRAINTS | HOJMAN TYPE | Peace movements | Analysis | Adiabatic flow | Mathematical analysis | Lie groups | Transformations | Perturbation | Equations of motion | Hamiltonian functions | Invariants | Nonlinear dynamics | Dynamical systems

Journal Article

Journal of Vibration and Control, ISSN 1077-5463, 1/2015, Volume 21, Issue 1, pp. 47 - 59

A procedure for designing a feedback control to asymptotically stabilize, with probability one, quasi-generalized Hamiltonian systems subject to stochastically...

stochastic stabilization | stochastic averaging | Feedback control | generalized Hamiltonian system | Lyapunov function | ACOUSTICS | VISCOELASTIC COLUMN | MECHANICS | FEEDBACK STABILIZATION | STABILITY | LYAPUNOV EXPONENT | ENGINEERING, MECHANICAL | Hamiltonian systems | Liapunov functions | Usage | Stochastic analysis | Stability | Asymptotic properties | Dynamics | Mathematical analysis | Mathematical models | Stochasticity | Dynamical systems

stochastic stabilization | stochastic averaging | Feedback control | generalized Hamiltonian system | Lyapunov function | ACOUSTICS | VISCOELASTIC COLUMN | MECHANICS | FEEDBACK STABILIZATION | STABILITY | LYAPUNOV EXPONENT | ENGINEERING, MECHANICAL | Hamiltonian systems | Liapunov functions | Usage | Stochastic analysis | Stability | Asymptotic properties | Dynamics | Mathematical analysis | Mathematical models | Stochasticity | Dynamical systems

Journal Article

Advances in Nonlinear Analysis, ISSN 2191-9496, 04/2017, Volume 8, Issue 1, pp. 372 - 385

Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case....

homoclinic solution | 34C37 | Hamiltonian system | 58E05 | Palais–Smale sequence | generalized Nehari manifold | MATHEMATICS | MATHEMATICS, APPLIED | Palais-Smale sequence

homoclinic solution | 34C37 | Hamiltonian system | 58E05 | Palais–Smale sequence | generalized Nehari manifold | MATHEMATICS | MATHEMATICS, APPLIED | Palais-Smale sequence

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 12/2013, Volume 57, pp. 105 - 111

We provide for a class of Hamiltonian systems in the action–angle variables sufficient conditions for showing the existence of periodic orbits. We expand this...

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2004, Volume 291, Issue 1, pp. 203 - 213

An existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order Hamiltonian systems u ̈ (t)−L(t)u(t)+∇W(t,u(t))=0 , ∀ t∈...

Second order Hamiltonian systems | Homoclinic solution | Superquadratic potentials | Generalized mountain pass theorem | homoclinic solution | second order Hamiltonian systems | MATHEMATICS | MATHEMATICS, APPLIED | superquadratic potentials | ORBITS | SIGN | generalized mountain pass theorem

Second order Hamiltonian systems | Homoclinic solution | Superquadratic potentials | Generalized mountain pass theorem | homoclinic solution | second order Hamiltonian systems | MATHEMATICS | MATHEMATICS, APPLIED | superquadratic potentials | ORBITS | SIGN | generalized mountain pass theorem

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 2, pp. 574 - 582

In this paper, we establish several new Lyapunov type inequalities for discrete linear Hamiltonian systems when the end-points are not necessarily usual zeros,...

Lyapunov inequality | Generalized zero | Stability | Discrete Hamiltonian system | CRITERIA | MATHEMATICS, APPLIED | TIME SCALES | DISCONJUGACY | DIFFERENCE-SYSTEMS | Mathematical models | Criteria | Computation | Optimization | Inequalities

Lyapunov inequality | Generalized zero | Stability | Discrete Hamiltonian system | CRITERIA | MATHEMATICS, APPLIED | TIME SCALES | DISCONJUGACY | DIFFERENCE-SYSTEMS | Mathematical models | Criteria | Computation | Optimization | Inequalities

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 04/2017, Volume 298, pp. 141 - 152

In this paper, we study bifurcation of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center. We use normal form theory to compute the...

Nilpotent center | Hopf bifurcation | Limit cycle | Normal form | Generalized Lyapunov constant | Near-Hamiltonian system | MATHEMATICS, APPLIED | FOCUS | DIFFERENTIAL-EQUATIONS | COMPUTATION | BIFURCATION | SIMPLEST NORMAL FORMS | Information science

Nilpotent center | Hopf bifurcation | Limit cycle | Normal form | Generalized Lyapunov constant | Near-Hamiltonian system | MATHEMATICS, APPLIED | FOCUS | DIFFERENTIAL-EQUATIONS | COMPUTATION | BIFURCATION | SIMPLEST NORMAL FORMS | Information science

Journal Article

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 11/2016, Volume 26, Issue 12, p. 1650204

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise...

limit cycle | Melnikov function | generalized eye-figure loop | Piecewise smooth Hamiltonian system | NUMBER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | VECTOR-FIELDS | DIFFERENTIAL-SYSTEMS | HILBERTS 16TH PROBLEM

limit cycle | Melnikov function | generalized eye-figure loop | Piecewise smooth Hamiltonian system | NUMBER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | VECTOR-FIELDS | DIFFERENTIAL-SYSTEMS | HILBERTS 16TH PROBLEM

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 01/2019, Volume 67, Issue 1, pp. 158 - 174

This paper analyses the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis...

Generalised Riccati equation | Hamiltonian system | 49N05 | LQ optimal control | 15A24 | 93C05 | MATHEMATICS | CONVERGENCE | CHEAP | Algebra | Riccati equation | Hamiltonian functions | Mathematical analysis | Optimal control

Generalised Riccati equation | Hamiltonian system | 49N05 | LQ optimal control | 15A24 | 93C05 | MATHEMATICS | CONVERGENCE | CHEAP | Algebra | Riccati equation | Hamiltonian functions | Mathematical analysis | Optimal control

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 4/2014, Volume 76, Issue 1, pp. 657 - 672

For a fractional generalized Hamiltonian system, in terms of Riesz derivatives, stability theory for the manifolds of equilibrium states is presented. The...

Fractional Hénon | Engineering | Vibration, Dynamical Systems, Control | Fractional generalized Hamiltonian system | Riesz derivative | Stability | Heiles model | Mechanics | Automotive Engineering | Manifold of equilibrium state | Mechanical Engineering | EQUATIONS | CONSERVED QUANTITY | FORMULATION | ENGINEERING, MECHANICAL | Fractional Henon | MECHANICS | SYMMETRY | LINEAR VELOCITIES | Manifolds | Equilibrium equations | Mathematical models | Representations | Hamiltonian functions | Equilibrium | Nonlinear dynamics | Dynamics | Mathematical analysis | Dynamical systems

Fractional Hénon | Engineering | Vibration, Dynamical Systems, Control | Fractional generalized Hamiltonian system | Riesz derivative | Stability | Heiles model | Mechanics | Automotive Engineering | Manifold of equilibrium state | Mechanical Engineering | EQUATIONS | CONSERVED QUANTITY | FORMULATION | ENGINEERING, MECHANICAL | Fractional Henon | MECHANICS | SYMMETRY | LINEAR VELOCITIES | Manifolds | Equilibrium equations | Mathematical models | Representations | Hamiltonian functions | Equilibrium | Nonlinear dynamics | Dynamics | Mathematical analysis | Dynamical systems

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 2014, Volume 34, Issue 9, pp. 3353 - 3369

Under the Ambrosetti-Rabinowitz's superquadraticy condition, or no Ambrosetti-Rabinowitz's superquadracity condition, we present two results on the existence...

Ground state | Hamiltonian system | Homoclinic orbits | Generalized fountain theorems | Generalized Nehari manifold | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | homoclinic orbits | generalized fountain theorems | THEOREMS | ground state | generalized Nehari manifold

Ground state | Hamiltonian system | Homoclinic orbits | Generalized fountain theorems | Generalized Nehari manifold | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | homoclinic orbits | generalized fountain theorems | THEOREMS | ground state | generalized Nehari manifold

Journal Article

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications, ISSN 2066-5997, 2018, Volume 10, Issue 1, pp. 41 - 58

In this paper we present a short description of the PhD thesis with the title ”Applications of Hamiltonian systems in analysis and optimization”. This thesis...

Approximation | Implicit systems | Generalized solution | Differential equations | Local parametrization | Implicit function theorem | Critical case | Numerical experiments | Constrained optimization | local parametrization | differential equa- tions | critical case | approxima- tion | numerical experiments | generalized solution | constrained optimization | implicit systems

Approximation | Implicit systems | Generalized solution | Differential equations | Local parametrization | Implicit function theorem | Critical case | Numerical experiments | Constrained optimization | local parametrization | differential equa- tions | critical case | approxima- tion | numerical experiments | generalized solution | constrained optimization | implicit systems

Journal Article

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