@article{Ma2023, 
author = {Cheng Ma},
title = {Normalized solutions for the mixed dispersion nonlinear Schrödinger equations with four types of potentials and mass subcritical growth},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {7},
pages = {3759-3775},
keywords = {biharmonic Schrödinger equations, normalized solution, variational method, constrained minimization technique},
url = {https://www.sciopen.com/article/10.3934/era.2023191},
doi = {10.3934/era.2023191},
abstract = {This paper is devoted to considering the attainability of minimizers of the        L    2  -constraint variational problem         m          γ      ,      a        =  inf    {      J          γ        (  u  )  :  u  ∈      H    2    (            R              N        )  ,      ∫                            R                          N                      |  u      |    2    d  x  =      a    2    }      ,  where         J          γ        (  u  )  =      γ    2        ∫                            R                          N                      |  Δ  u      |    2    d  x  +      1    2        ∫                            R                          N                      |  ∇  u      |    2    d  x  +      1    2        ∫                            R                          N                      V  (  x  )  |  u      |    2    d  x  −      1          2      σ      +      2            ∫                            R                          N                      |  u      |          2      σ      +      2        d  x  ,   γ  >  0,    a  >  0,    σ  ∈  (  0  ,      2    N    ) with    N  ≥  2. Moreover, the function    V  :            R              N        →  [  0  ,  +  ∞  ) is continuous and bounded. By using the variational methods, we can prove that, when    V satisfies four different assumptions,        m          γ      ,      a       are all achieved.}
}