Infinitely many homoclinic orbits for discrete Hamiltonian systems with subquadratic potential

摘要

In this paper, we deal with the existence of infinitely many homoclinic solutions for the second-order self-adjoint discrete Hamiltonian system where and are real symmetric matrices for all, and is always positive definite. Under the assumptions that is indefinite sign and subquadratic as and satisfies for some constant, we establish an existence criterion to guarantee that the above system has infinitely many homoclinic solutions.