On ground state solutions for some non-autonomous Schrödinger–Poisson systems

Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well

“…Later, Sun et al 31 also studied system (1.2) with asymptotically linear nonlinearity a(x) f (u). They obtained the existence of positive ground state solutions under suitable K ∈ L 2 (R 3 ) and a(x) by the mountain pass theorem.…”

Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth

“…2 ) by (25). In the case of non-vanishing, we can follow the similar idea in [21] to construct a minimizer.…”

Multiple Symmetric Results for Quasilinear Elliptic Systems Involving Singular Potentials and Critical Sobolev Exponents inRN

“…Firstly, we choose > 0 such that the condition (17) holds, where is the extremal function satisfying (10), (11), and (12). By (q.1), (23), and (25), we have…”

“…Very recently, Nyamoradi [16], Lü and Xiao [17], and Li and Gao [18] generalized the corresponding results of [15] to the nonlinear singular elliptic systems involving critical Hardy-Sobolev exponents. Other results about existence and multiplicity of nontrivial solutions, also for related elliptic systems, can be seen in [19][20][21][22][23] and the references therein.…”