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Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity
Author(s) -
Gu Guangze,
Tang Xianhua,
Yang Xianyong
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900273
Subject(s) - mathematics , infinity , mathematical analysis , operator (biology) , nonlinear system , laplace's equation , laplace transform , partial differential equation , physics , chemistry , repressor , quantum mechanics , transcription factor , gene , biochemistry
In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearitya + b ∫ R 3( − Δ ) s 2 u 2d x( − Δ ) s u + V ( x ) u = Q ( x ) f ( u ) + | u |2 s ∗ − 2 u , x ∈ R 3 ,where a , b > 0 ,( − Δ ) s is the fractional Laplace operator with s ∈ ( 3 4 , 1 ) , V vanishes at infinity and2 s ∗ = 6 3 − 2 s. Under appropriate assumptions on f , we prove the existence of positive solution by using the variational method.