scholarly journals The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

1997 ◽  
Vol 349 (7) ◽  
pp. 2619-2661 ◽  
Author(s):  
Di Dong ◽  
Yiming Long
Keyword(s):  
Hamiltonian Systems ◽  
Index Theory ◽  
Iteration Formula

scholarly journals Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Qi Wang ◽  
Qingye Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Index Theory ◽  
Maslov Index ◽  
Homoclinic Orbits ◽  
Asymptotically Linear ◽  
Existence And Multiplicity ◽  
Hamiltonian Functions

By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.

Maslov (P, ω)-Index Theory for Symplectic Paths

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Chungen Liu ◽  
Shanshan Tang
Keyword(s):  
Index Theory ◽  
Iteration Formula ◽  
Symplectic Path

AbstractIn this paper, the Maslov (P, ω)-index theory for a symplectic path is developed and the Bott-type iteration formula is proved.

scholarly journals Existence of solutions for subquadratic convex operator equations at resonance and applications to Hamiltonian systems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingliang Song ◽  
Ping Chen
Keyword(s):  
Hamiltonian Systems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Index Theory ◽  
Linear Operators ◽  
Least Action Principle ◽  
Operator Equations ◽  
Least Action ◽  
Special Cases ◽  
Sturm Liouville

Abstract This paper investigates the existence of solutions to subquadratic operator equations with convex nonlinearities and resonance by means of the index theory for self-adjoint linear operators developed by Dong and dual least action principle developed by Clarke and Ekeland. Applying the results to subquadratic convex Hamiltonian systems satisfying several boundary value conditions including Bolza boundary value conditions, generalized periodic boundary value conditions and Sturm–Liouville boundary value conditions yield some new theorems concerning the existence of solutions or nontrivial solutions. In particular, some famous results about solutions to subquadratic convex Hamiltonian systems by Mawhin and Willem and Ekeland are special cases of the theorems.

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