@article{Shu2024, 
author = {Zhidan Shu and Jianjun Zhang},
title = {Normalized multi-bump solutions of nonlinear Kirchhoff equations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {16790-16809},
keywords = {Kirchhoff equation, normalized solutions, concentration behavior},
url = {https://www.sciopen.com/article/10.3934/math.2024814},
doi = {10.3934/math.2024814},
abstract = {We are concerned with the existence and concentration of multi-bump solutions for the nonlinear Kirchhoff equation                       −                  (                                    ε                              2                                      a            +            ε            b                                                            ∫                                                                                            R                                                              3                                                                                                                    |                                      ∇                    v                                    |                                                  2                                                            d                            x                                )                Δ        v        +        λ        v        =        K        (        x        )                              |            v            |                                2            σ                          v        ,                                x        ∈                              R                    3                    with an        L          2      -constraint in the        L          2      -subcritical case    σ  ∈      (          0      ,                    2        3              )   and the        L          2      -supercritical case    σ  ∈      (                  2        3            ,            2        )    . Here    λ  ∈      R   appears as a Lagrange multiplier,    ε is a small positive parameter and    K  >  0 possesses several local maximum points. By employing the variational gluing method and the penalization technique, we prove the existence of multi-bump solutions that are concentrated at local maximum points of    K for the problem above.}
}