Multiple solutions for asymptotically quadratic and superquadratic elliptic system of Hamiltonian type

Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity

“…Assuming that V is periodic and positive, nontrivial solutions were obtained by Liao et al in the recent paper [22] under some new super-quadratic conditions. The nonperiodic and asymptotically quadratic case was studied in [36,41,42]. For semiclassical problems with subcritical and critical nonlinearities, we refer to [14,22].…”

“…, and there exist constants p ∈ (2, 2 * ) and C 1 > 0 such that Condition (DL) was first introduced by Ding and Lee [13] for a single Schrödinger equation, and it together with (SQ) is commonly used instead of the following classic condition, see, for instance, [26,40,42].…”

“…The idea of using the more natural super-quadratic condition (SQ) under a Nehari type setting to replace (AR) goes back to Liu and Wang [25]. Afterwards, condition (SQ) was used in many papers, see [13,14,26,33,38,42,47] and the references therein. In a recent paper [30], a local superquadratic condition instead of (SQ) was introduced by Qin, Tang, and Wu, which combines with a technical condition to guarantee the existence of ground state solutions for Schrödinger systems like (1.1).…”

Ground state solutions of Nehari‐Pankov type for a superlinear elliptic system on

“…a minimizer of the corresponding energy within the set of nontrivial solutions) or multiple solutions were obtained for problem (1) with periodic potential and nonlinearity, see [16,18,22,24,26,[28][29][30][31][38][39][40]. For the non-periodic case, we refer the readers to [20,21,25,32,41] and the references therein.…”