Homoclinic orbits for an unbounded superquadratic

Abstract

Abstract. We consider the following nonperiodic diffusion systems Gv(t, x, u, v), Gu(t, x, u, v),whereSuppose that the potential V is positive constant and G(t, x, z) is superquadratic in z as |z| → ∞. By applying a generalized linking theorem for strongly indefinite functionals, we obtain homoclinic solutions z satisfying z(t, x) → 0 as |(t, x)| → ∞. Mathematics Subject Classification (2000). 58E50 (Variational problems in infinite-dimensional spaces, Applications).

Ground state solutions for a diffusion system

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

“…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…”