Normalized Solutions to Nonautonomous Kirchhoff Equation

2023/10/25 by Qiu, Xin, Ou, Zeng-Qi, Lv, Ying
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.16359

Abstract

In this paper, we study the existence of normalized solutions to the following Kirchhoff equation with a perturbation: \ \beginaligned amp;-(a+b∫ _ℝ^N | ∇ u |² dx)Δu+λu=|u|^p-2 u+h(x) |u |^q-2u, in ℝ^N,
amp;∫_ℝ^N|u|²dx=c, u ∈ H¹(ℝ^N), \endaligned . where 1≤ N≤ 3, a,b,c>0, 1≤ q<2, λ∈ ℝ. We treat three cases. (i)When 2

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