摘要：We study the existence of homoclinic solutions for the following second-order self-adjoint discrete Hamiltonian system: △ [ p ( n ) △ u ( n − 1 ) ] − L ( n ) u ( n ) + ∇ W ( n , u ( n ) ) = 0 $\triangle[p(n)\triangle u(n-1)]-L(n)u(n)+\nabla W(n, u(n))=0$ , where p ( n ) $p(n)$ , L ( n ) $L(n)$ , and W ( n , x ) $W(n, x)$ are N-periodic in n, and ∇ W ( n , x ) $\nabla W(n, x)$ is asymptotically linear in x as x → ∞ $ x \to\infty$ .
关键词：homoclinic solution ; discrete Hamiltonian system ; asymptotically linear ; strongly indefinite functional
