scholarly journals New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Xuefeng Li ◽  
Jin Jia
Keyword(s):  
Hamiltonian Systems ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Mixed Condition ◽  
Second Order Hamiltonian Systems

Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems

2017 ◽  
Vol 8 (1) ◽  
pp. 372-385
Author(s):  
Alexander Pankov
Keyword(s):  
Hamiltonian Systems ◽  
Careful Analysis ◽  
Energy Functional ◽  
Nehari Manifold ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Almost Periodic ◽  
Second Order Hamiltonian Systems

Abstract Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case. The proof relies on a careful analysis of the energy functional restricted to the generalized Nehari manifold, and the existence and fine properties of special Palais–Smale sequences.

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