Multi-peak positive solutions for the fractional Schrödinger–Poisson system

Abstract

In this paper, we study the existence of positive multi-peak solutions to the fractional Schrödinger–Poisson system [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text] is a positive function, [Formula: see text] and [Formula: see text] Under some given conditions which are given in Sec. ??, we prove the existence of a positive solution with m-peaks and concentrating near a given local maximum point of [Formula: see text]

Existence and concentration of positive ground state solutions for nonlinear fractional Schrödinger‐Poisson system with critical growth

“…For this reason, (1.2) is referred to as a nonlinear Schrödinger-Poisson system. In recent years, there has been increasing attention to systems like (1.2) on the existence of positive solutions, ground state solutions, multiple solutions, and semiclassical states; see, for example, previous studies [4][5][6][7][8][9][10][11][12][13] and the references therein.…”

Boundary concentration of peak solutions for fractional Schrödinger-Poisson system

“…When s = 1 and Ω = R 3 , (1.1) has been investigated by [59] and also [53] for Ω = R N (3 ≤ N ≤ 6), and [10,36,39,40,62] for different potentials. When s ∈ (0, 1) and Ω = R 3 , (1.1) has received much attentions, see [38,46,47,48,49,50,51,54] and references therein. The previous results are constructing single or multiply peak solutions whose peaks concentrate near the critical points of potentials.…”