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Home » Infinitely many homoclinic orbits for a class of discrete Hamiltonian systems

  1. Infinitely many homoclinic orbits for a class of discrete Hamiltonian systems

    Author Name: Xianhua Tang, Jing Chen

    In the present paper, we deal with the existence of infinitely many homoclinic solutions for the second-order self-adjoint discrete Hamiltonian system $$ \triangle [p(n)\triangle u(n-1)]-L(n)u(n)+\nabla W(n, u(n))=0, $$ where $p(n)$ and $L(n)$ are $\mathcal{N}\times \mathcal{N}$ real symmetric matrices for all $n\in \Z$, and $p(n)$ is always positive definite. Under the assumptions that $L(n)$ is allowed to be sign-changing and satisfies $$ \lim_{|n|\to +\infty}\inf_{|x|=1}(L(n)x, x)=\infty, $$ $W(n, x)$ is of indefinite sign and superquadratic as $|x|\to +\infty$, we establish several existence criteria to guarantee that the above system has infinitely many homoclinic solutions..

    Date of published: 2013-09-27

    Journal Name: Advances In Difference Equations

    DOI: Not Available

    Keywords: Advances In Difference Equations

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