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- Title
Uniqueness of Single Peak Solutions for a Kirchhoff Equation.
- Authors
Lv, Junhao; Yi, Shichao; Sun, Bo
- 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.
- Subjects
SINGULAR perturbations; PERTURBATION theory; EQUATIONS
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 10, p1462
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12101462