Positive solutions for fractional Kirchhoff–Schrödinger–Poisson system with steep potential well

Abstract

In this paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system: [Formula: see text] where [Formula: see text] and [Formula: see text] is a constant, [Formula: see text] are positive parameters, [Formula: see text] represents a potential well with the bottom [Formula: see text]. By applying the truncation technique and the parameter-dependent compactness lemma, we first prove the existence of positive solutions for b small, [Formula: see text] large and [Formula: see text] small in the case [Formula: see text]. Moreover, we investigate the decay rate of positive solutions as [Formula: see text] as well as their asymptotic behavior as [Formula: see text] and [Formula: see text], respectively.