Normalized solutions for a fourth-order Schrődinger equation with a positive second-order dispersion coefficient  

作　　者：Xiao Luo Tao Yang 

机构地区：[1]School of Mathematics,Hefei University of Technology,Hefei 230009,China [2]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Science China Mathematics》2023年第6期1237-1262,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11901147);the Fundamental Research Funds for the Central Universities of China (Grant No.JZ2020HGTB0030)。

摘　　要：In this paper,we study normalized solutions to a fourth-order Schrődinger equation with a positive second-order dispersion coefficient in the mass supercritical regime.Unlike the well-studied case where the second-order term is zero or negative,the geometrical structure of the corresponding energy functional changes dramatically and this makes the solution set richer.Under suitable control of the second-order dispersion coefficient and mass,we find at least two radial normalized solutions,a ground state and an excited state,together with some asymptotic properties.It is worth pointing out that in the considered repulsive case,the compactness analysis of the related Palais-Smale sequences becomes more challenging.This forces the implementation of refined estimates of the Lagrange multiplier and the energy level to obtain normalized solutions.

关 键 词：fourth-order Schrodinger equation mixed dispersion normalized solution variational method 

分 类 号：O175.29[理学—数学]