An index theory with applications to homoclinic orbits of Hamiltonian systems and Dirac equations
DOI10.1007/s10884-020-09846-3zbMath1446.49028arXiv1802.03492OpenAlexW3015077732MaRDI QIDQ785369
Publication date: 6 August 2020
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1802.03492
index theorynonlinear Dirac equationsdual variational methodshomoclinic orbits for Hamiltonian system
Variational methods involving nonlinear operators (47J30) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Eigenvalue problems for linear operators (47A75) Duality theory (optimization) (49N15) Time-dependent Schrödinger equations and Dirac equations (35Q41) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence of ground state solutions to Dirac equations with vanishing potentials at infinity
- Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero
- Homoclinic orbits of nonperiodic superquadratic Hamiltonian system
- Infinitely many homoclinic orbits for superlinear Hamiltonian systems
- Homoclinic orbits for the first-order Hamiltonian system with superquadratic nonlinearity
- Homoclinic orbits for a class of first-order nonperiodic asymptotically quadratic Hamiltonian systems with spectrum point zero
- Multiplicity of closed characteristics on symmetric convex hypersurfaces in \(\mathbb{R}^{2n}\)
- Une théorie de Morse pour les systèmes hamiltoniens convexes
- A variational approach to homoclinic orbits in Hamiltonian systems
- A new index theory for linear self-adjoint operator equations and its applications
- The relative Morse index theory for infinite dimensional Hamiltonian systems with applications
- Existence of stationary states for nonlinear Dirac equations
- First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems
- Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition
- Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations
- Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system
- Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems
- Convex Hamiltonian energy surfaces and their periodic trajectories
- Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
- Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits
- Looking for the Bernoulli shift
- Nontrivial periodic solutions for strong resonance Hamiltonian systems
- A Maslov-type index theory for symplectic paths
- Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
- Infinite dimensional Morse theory and multiple solution problems
- Homoclinic solutions of Hamiltonian systems with symmetry
- Homoclinic orbits of a Hamiltonian system
- Homoclinic orbits for first order Hamiltonian systems
- Relative Morse index and its application to Hamiltonian systems in the presence of symmetries
- Stationary states of the nonlinear Dirac equation: A variational approach
- Maslov-type index theory for symplectic paths and spectral flow. II
- Maslov-type index theory for symplectic paths and spectral flow. I
- Localized concentration of semi-classical states for nonlinear Dirac equations
- Homoclinic orbits for a nonperiodic Hamiltonian system
- Periodic solutions of delay differential systems via Hamiltonian systems
- Solutions of nonlinear Dirac equations
- Maslov index for homoclinic orbits of Hamiltonian systems
- An index theory for symplectic paths associated with two Lagrangian subspaces with applications
- Homoclinic orbits of superlinear Hamiltonian systems
- STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS
- Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
- Infinitely many homoclinic orbits of a Hamiltonian system with symmetry
- 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
- MULTIPLE HOMOCLINICS IN A HAMILTONIAN SYSTEM WITH ASYMPTOTICALLY OR SUPER LINEAR TERMS
- Maslov-Type Index Theory For Symplectic Paths With Lagrangian Boundary Conditions
- Existence of infinitely many homoclinic orbits in Hamiltonian systems
- Homoclinic orbits for asymptotically linear Hamiltonian systems