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Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three

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 {(abΩ|u|2dx)Δu=λ|u|p2u+|u|4u,xΩ,u=0,xΩ, 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 b0.

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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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