Homoclinic orbits for second-order discrete Hamiltonian systems with subquadratic potential

摘要

Under the assumptions that W ( n , x ) is indefinite sign and subquadratic as | x | → + ∞ and L ( n ) satisfies lim?inf | n | → + ∞ [ | n | ν ? 2 inf | x | = 1 ( L ( n ) x , x ) ] > 0 for some constant ν < 2 , we establish a theorem on the existence of infinitely many homoclinic solutions for the second-order self-adjoint discrete Hamiltonian system △ [ p ( n ) △ u ( n ? 1 ) ] ? L ( n ) u ( n ) + ? W ( n , u ( n ) ) = 0 , where p ( n ) and L ( n ) are N × N real symmetric matrices for all n ∈ Z , and p ( n ) is always positive definite. MSC:39A11, 58E05, 70H05.