Infinitely many homoclinic orbits for a class of discrete Hamiltonian systems

摘要

In the present paper, we deal with 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. Under the assumptions that L ( n ) is allowed to be sign-changing and satisfies lim | n | → + ∞ inf | x | = 1 ( L ( n ) x , x ) = ∞ , W ( n , x ) is of indefinite sign and superquadratic as | x | → + ∞ , we establish several existence criteria to guarantee that the above system has infinitely many homoclinic solutions. MSC:39A11, 58E05, 70H05.