@article{Wang2022, 
author = {Zhongxiang Wang},
title = {Existence and asymptotic behavior of normalized solutions for the modified Kirchhoff equations in              R        3},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {8774-8801},
keywords = {modified Kirchhoff-type equations, L2-normalized solutions, asymptotic behavior, constrained minimization method, perturbation method},
url = {https://www.sciopen.com/article/10.3934/math.2022490},
doi = {10.3934/math.2022490},
abstract = {This paper is concerned with the following modified Kirchhoff type problem                       −                  (                      a            +            b                          ∫                                                                    R                                    3                                                                    |                        ∇            u                                          |                            2                                )                Δ        u        −        u        Δ        (                  u          2                )        −        λ        u        =                  |                u                              |                                p            −            2                          u        ,                                x        ∈                              R                    3                ,            where    a  ,  b  >  0 are constants and    λ  ∈      R  . When    p  =      16    3  , we prove that the existence of normalized solution with a prescribed        L    2  -norm for the above equation by applying constrained minimization method. Moreover, when    p  ∈      (                  10        3            ,              16        3              )  , we prove the existence of mountain pass type normalized solution for the above modified Kirchhoff equation by using the perturbation method. And the asymptotic behavior of normalized solution as    b  →  0 is analyzed. These conclusions extend some known ones in previous papers.}
}