The concentration behavior of ground state solutions for a critical fractional Schrödinger–Poisson system

Zhipeng Yang, Yuanyang Yu and Fukun Zhao

Mathematische Nachrichten, 2019, vol. 292, issue 8, 1837-1868

Abstract: In this paper, we study the following critical fractional Schrödinger–Poisson system ε2s(−Δ)su+V(x)u+ϕu=P(x)f(u)+Q(x)|u|2s∗−2u,inR3,ε2t(−Δ)tϕ=u2,inR3,where ε>0 is a small parameter, s∈(34,1),t∈(0,1) and 2s+2t>3, 2s∗:=63−2s is the fractional critical exponent for 3‐dimension, V(x)∈C(R3) has a positive global minimum, and P(x),Q(x)∈C(R3) are positive and have global maximums. We obtain the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials V,P and Q as the concentration position of these ground state solutions as ε→0+. Moreover, we consider some properties of these ground state solutions, such as convergence and decay estimate.

Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1002/mana.201700398

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:292:y:2019:i:8:p:1837-1868

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().