Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity

We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation −(a+b∫RN|∇u|2)Δu+λu=uq−1+up−1inRN,(Pλ)as λ→0 and λ→+∞, where N=3 or N=4, 20, b≥0 are constants and λ>0 is a parameter. In particular, we prove that in the case 2

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Bibliographic Details
Published in:Nonlinear analysis 2024-02, Vol.239, p.113423, Article 113423
Main Authors: Ma, Shiwang, Moroz, Vitaly
Format: Article
Language:English
Subjects:
Asymptotic behavior
Concentration compactness
Critical Sobolev exponent
Mass L2-critical exponent
Nonlinear Kirchhoff equation
Normalized solutions
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Summary:We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation −(a+b∫RN|∇u|2)Δu+λu=uq−1+up−1inRN,(Pλ)as λ→0 and λ→+∞, where N=3 or N=4, 20, b≥0 are constants and λ>0 is a parameter. In particular, we prove that in the case 2
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2023.113423