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Uniqueness of Single Peak Solutions for a Kirchhoff Equation

Author

Listed:
  • 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
    Yangzijiang Shipbuilding Group, Taizhou 212299, China)

  • Bo Sun

    (School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China)

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.

Suggested Citation

  • Junhao Lv & Shichao Yi & Bo Sun, 2024. "Uniqueness of Single Peak Solutions for a Kirchhoff Equation," Mathematics, MDPI, vol. 12(10), pages 1-7, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1462-:d:1390791
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