Uniqueness of Single Peak Solutions for a Kirchhoff Equation

Junhao Lv, Shichao Yi () and Bo Sun
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Junhao Lv: School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Shichao Yi: School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Bo Sun: School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Mathematics, 2024, vol. 12, issue 10, 1-7

Abstract: We deal with the following singular perturbation Kirchhoff equation: − ϵ 2 a + ϵ b ∫ R 3 | ∇ u | 2 d y Δ u + Q ( y ) u = | u | p − 1 u , u ∈ H 1 ( R 3 ) , where constants a , b , ϵ > 0 and 1 < p < 5 . In this paper, we prove the uniqueness of the concentrated solutions under some suitable assumptions on asymptotic behaviors of Q ( y ) and its first derivatives by using a type of Pohozaev identity for a small enough ϵ . To some extent, our result exhibits a new phenomenon for a kind of Q ( x ) which allows for different orders in different directions.

Keywords: Kirchhoff equations; single-peak solutions; uniqueness; Pohozaev identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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