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

Abstract

For a class of asymptotically periodic Schrödinger-Poisson systems with critical growth, the existence of ground states is established. The proof is based on the method of Nehari manifold and concentration compactness principle. MSC:35J05, 35J50, 35J60

WITHDRAWN: New super-quadratic conditions for asymptotically periodic Schrödinger equation

“…Motivated by the works [7,13,15,25,26,27,33], we shall find new tricks to overcome the difficulties caused by the dropping of periodicity of V (x).…”

Quasilinear asymptotically periodic Schrödinger–Poisson system with subcritical growth

“…System (1.1) without quasilinear potential -u (u 2 ) is called the Schrödinger-Poisson system, u + V (x)u + K(x)φ(x)u = g(x, u), x ∈ R 3 , φ = K(x)u 2 , x ∈ R 3 , which has been widely studied, and many meaningful results were achieved for the subcritical growth [7,27,44,45,47] or the critical exponent [46] under various assumptions on the potentials and nonlinearities. Furthermore, nontrivial solutions, radial solutions [10,13,29], ground state solutions [2,4] and also semiclassical solutions [14,23,24] were obtained generally.…”

New multiple solutions for a Schrödinger–Poisson system involving concave-convex nonlinearities

“…In recent years, the following form of Schrödinger-Poisson system with critical growth { −△u + V (x)u + K(x)φu = Q(x)u 5 + f (x, u), in R 3 , −△φ = K(x)u 2 , in R 3 , has been investigated extensively. For previous related results, please refer to [1,4,12,15,[17][18][19]23]. Further, the Schrödinger-Poisson system with concave-convex nonlinearities has attracted much attention.…”