Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 1
164
Views
4
CrossRef citations to date
0
Altmetric
Research Article

Multiplicity and concentration of solutions for a fractional Schrödinger–Poisson system with sign-changing potential

&
Pages 253-274 | Received 08 Sep 2020, Accepted 23 Jun 2021, Published online: 08 Jul 2021
 

Abstract

This paper is concerned with the following fractional Schrödinger–Poisson system: {(Δ)αu+Vλ(x)u+μϕu=f(x,u)+β(x)|u|ν2uinR3,(Δ)tϕ=u2inR3,where μ>0 is a parameter, α,t(0,1), ν(1,2), 2α+2t>3, Vλ is allowed to be sign-changing and f is an indefinite function. We require that Vλ(x)=λV+(x)V(x) with V+(x) having a potential well Ω whose depth is controlled by λ and V(x)0 for all xR3. Under some suitable assumptions on Vλ(x) and f(x,u), we prove that the above system has at least two nontrivial solutions. Moreover, the phenomenon of concentration of the solutions is also explored.

2010 Mathematics Subject Classifications:

Acknowledgments

The authors thank the referees for carefully reading the manuscript, giving valuable comments and suggestions to improve the results as well as the exposition of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant No. 12001114, 12071486] and the Guangdong Basic and Applied Basic Research Foundation [Grant No. 2019A1515110275].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.