Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three
Year: 2022
Author: Xiaotao Qian
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 382–394
Abstract
In this paper, we are interested in the following nonlocal problem with critical exponent {−(a−b∫Ω|∇u|2dx)Δu=λ|u|p−2u+|u|4u,x∈Ω,u=0,x∈∂Ω, where a,b are positive constants, 2<p<6, Ω is a smooth bounded domain in R3 and λ>0 is a parameter. By variational methods, we prove that problem has a positive ground state solution ub for λ>0 sufficiently large. Moreover, we take b as a parameter and study the asymptotic behavior of ub when b↘0.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n4.6
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 382–394
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Nonlocal problem critical exponent positive solutions variational methods.
Author Details
Xiaotao Qian Email
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Qian, Xiaotao
Shi, Zhigao
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