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Homoclinic solutions for second‐order discrete Hamiltonian systems with asymptotically quadratic potentials
Author(s) -
Chen Huiwen,
He Zhimin
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2989
Subject(s) - homoclinic orbit , mathematics , hamiltonian system , quadratic equation , order (exchange) , pure mathematics , hamiltonian (control theory) , fountain , mathematical analysis , mathematical optimization , bifurcation , physics , geometry , finance , quantum mechanics , nonlinear system , economics , archaeology , history
In this paper, we study the existence of infinitely many homoclinic solutions for the second‐order self‐adjoint discrete Hamiltonian system Δ 2 u ( n − 1 ) − L ( n ) u ( n ) + ∇ W ( n , u ( n ) ) = 0 , where n ∈ Z , u ∈ R N and L : ℤ → ℝ N × Nare unnecessarily positive definites for all n ∈ Z . By using the variant fountain theorem, we obtain an existence criterion to guarantee that the aforementioned system has infinitely many homoclinic solutions under the assumption that W ( n , x ) is asymptotically quadratic as | x | → + ∞ . Copyright © 2013 John Wiley & Sons, Ltd.
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