Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity

2022/11/27 by Shiwang Ma, Vitaly Moroz, Ma, Shiwang +1
Mathematics · #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2211.14895

Abstract

We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation -(a+b∫_{\mathbb R^N}|∇ u|²)Δu+ λu= u^q-1+ u^p-1 \rm in \mathbb R^N, 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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