On a class of infinite-dimensional Hamiltonian systems with asymptotically periodic nonlinearities

Abstract

The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × R N : Hu(t, x, u, v),. Under suitable conditions on V (t, x) and the nonlinearity for H (t, x, z), at least one non-stationary homoclinic solution with least energy is obtained.

Ground state solutions for a diffusion system

“…The problem in the whole space R N was considered in some works. For example, see [9][10][11][12][13][14][15][16][17][18][19][20]. Bartsch and Ding [9] investigated the following infinite-dimensional Hamiltonian system…”

“…For the related works about the system with gradient terms, we refer to [11,15,16,14,17,19] and the references therein.…”

Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system

“…Especially the variational method and other topological methods have attracted considerable attention in the existence of the solution of the reaction-diffusion system. See [1,2,17,5,6,7,8,11,9,12,13,14,19,23,27,28,31,29,30,33]. However, to our best knowledge, there is few work on the existence of nonstationary solutions for systems such as (1).…”