A perturbation result for the energy critical Choquard equation in ℝ^N

2023/07/02 by Xinyu Bo, Guangying Lv, Bo, Xinyu +5
Engineering · Mathematics · #2010: 35B25 #35B09 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.00564

openalex publication_date 2023/07/02 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28

Abstract

We study the singularly perturbed nonlinear energy critical Choquard equation -\Laplace u\qty(x) -α ∫_\R^N\fracu^p\qty(y)\absx-y^λ\odify u^p-1\qty(x) -\eps k\qty(x)u^(N+2)/(N-2)\qty(x)=0, x∈\R^N, where N≥ 3, 0<λ0, we construct solutions of the form u_\eps\qty(x)=U_μ_\eps,ξ_\eps\qty(x)\qty(1+Ø\qty(\eps)), where U_μ_\eps,ξ_\eps is a positive solution of the unperturbed equation -\Laplace u\qty(x) -α ∫_\R^N\fracu^p\qty(y)\absx-y^λ\odify=0, x∈\R^N.

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