Homoclinic solutions for second-order discrete Hamiltonian systems with asymptotically quadratic potentials

作者：Chen, Huiwen; He, Zhimin^*

来源：Mathematical Methods in the Applied Sciences, 2014, 37(16): 2451-2462.

DOI：10.1002/mma.2989

• homoclinic solutions
• discrete Hamiltonian systems
• variational methods
• asymptotically quadratic

In this paper, we study the existence of infinitely many homoclinic solutions for the second-order self-adjoint discrete Hamiltonian system Delta(2)u(n - 1) - L(n)u(n) + del W(n, u(n)) = 0, where n is an element of Z, u is an element of R-N and L : Z -> R-NxN are unnecessarily positive definites for all n is an element of 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 vertical bar x vertical bar -> +infinity.

• 出版日期2014-11-15
• 单位中南大学