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

Hui Jian

https://orcid.org/0000-0002-7688-6114

College of Science, East China Jiaotong University, Nanchang, 330013, P. R. China

E-mail Address: jianhui0711141@163.com

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Qiaocheng Zhong

https://orcid.org/0000-0002-9141-9549

College of Science, East China Jiaotong University, Nanchang, 330013, P. R. China

E-mail Address: 1097743227@qq.com

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, and

Li Wang

https://orcid.org/0000-0002-8370-9327

College of Science, East China Jiaotong University, Nanchang, 330013, P. R. China

E-mail Address: wangli.423@163.com

Corresponding author.

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https://doi.org/10.1142/S0129055X23500241Cited by:0 (Source: Crossref)

Abstract

In this paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system:

where

$s \in [\frac{3}{4}, 1), t \in (0, 1), 2 < p < 4$ and

$a > 0$ is a constant,

$b, λ, μ$ are positive parameters,

$V (x)$ represents a potential well with the bottom

$V^{- 1} (0)$ . By applying the truncation technique and the parameter-dependent compactness lemma, we first prove the existence of positive solutions for b small,

$λ$ large and

$μ$ small in the case

$2 < p < 4$ . Moreover, we investigate the decay rate of positive solutions as

$| x | \to \infty$ as well as their asymptotic behavior as

$b \to 0, λ \to \infty$ and

$μ \to 0$ , respectively.

Keywords:

AMSC: 35J20, 35J60, 35B40, 35R11

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Vol. 35, No. 07

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History

Received 25 March 2022

Revised 30 April 2023

Accepted 14 June 2023

Published: 15 July 2023

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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

Abstract

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