Homoclinic orbits for an infinite dimensional Hamiltonian system with periodic potential

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…”

“…Additionally, Zhang et al [20] gave a different method and generalized the result in [18] by weakening condition (S 3 ) to a weaker condition (S 4 ): (S 4 ) s → f (t, x, s)/|s| and s → g(t, x, s)/|s| are non-decreasing on (−∞, 0) and (0, +∞).…”

“…Motivated by papers [18,20,22], we will continue to study the existence of ground state solutions of problem (1.1) under some weaker conditions. More precisely, we make the following assumptions:…”

“…Therefore, our condition can be applied to more general situations. Moreover, it is worth pointing out that the following inequality in [18,20] is very important in proving the boundedness of Palais-Smale sequences or Cerami sequences, i.e.,…”

“…The proof was given in [11,20], here we omit the details. Now we discuss the linking structure of Φ.…”