MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE FRACTIONAL SCHRODINGER-POISSON SYSTEM WITH DOUBLY CRITICAL GROWTH

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外文摘要：In this paper,we are concerned with solutions to the fractional Schrödinger-Poisson system{(-Δ)su-φ|u|2*s-3u=λu+μ|u|q-2u+|u|2*s-2u,x ∈ R3,(-Δ)sφ=|u|2*s-1,x ∈ R3,with prescribed mass ∫R3|u|2dx=a2,where a＞0 is a prescribed number,p＞0 is a paremeter,s ∈(0,1),2＜q＜2*,and 2*=362is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L2-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrödinger-Poisson system with a nonlocal critical term.

外文关键词：

fractional Schrödinger-Poisson systemnormalized solutionsvariational meth-odsL2-subcriticalL2-supercritical

作者：

孟禹希、贺小明

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作者单位：

School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China

College of Science,Minzu University of China,Beijing 100081,China

基金：

BIT Research and Innovation Promoting ProjectNSFCNSFCNSFCNSFCNSFCBNSFFundamental Research Funds for the Central Universities

项目编号：

2023YCXY04611771468119710271197106112171497122710281222017

出版年：

2024

DOI：

10.1007/s10473-024-0313-x

数学物理学报(英文版)

中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD

影响因子：0.256

ISSN：0252-9602

年,卷(期)：2024.44(3)