含混合项的拟线性Schrödinger方程的正规化基态解

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 1062-1072.

含混合项的拟线性Schrödinger方程的正规化基态解

归坤明(),陶虹杉(),杨俊^*()

华南理工大学数学学院广州 510640

收稿日期:2022-06-17 修回日期:2023-01-12 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 杨俊 E-mail:guikunming@qq.com;sora1924@outlook.com;yangjun@scut.edu.cn
作者简介:归坤明，E-mail: guikunming@qq.com;|陶虹杉，sora1924@outlook.com
基金资助:
广东省自然科学基金(2018A0303130196)

Normalized Ground States for the Quasi-linear Schrödinger Equation with Combined Nonlinearities

Gui Kunming(),Tao Hongshan(),Yang Jun^*()

School of Mathematics, South China University of Technology, Guangzhou 510640

Received:2022-06-17 Revised:2023-01-12 Online:2023-08-26 Published:2023-07-03
Contact: Jun Yang E-mail:guikunming@qq.com;sora1924@outlook.com;yangjun@scut.edu.cn
Supported by:
NSF of Guangdong Province(2018A0303130196)

摘要/Abstract

摘要：

该文研究了一类含混合项拟线性Schrödinger方程正规化基态解的存在性. 推广了文献^[1-2]中的结果, 与他们研究的情形相比, 该文中方程对应能量泛函的结构更加复杂.

关键词: 正规化解, 拟线性Schr?dinger方程, 摄动法

Abstract:

In this paper, we mainly investigate the existence of normalized ground states for the Schrödinger equation with combined nonlinearities. Our results extend those reported in ^[1-2]. Compared with the case they studied, the structure of the energy function correspongding to the equation in this paper is more complex.

Key words: Normalized solutions, Quasi-linear Schr?dinger equation, Perturbation method

中图分类号:

O175.29

归坤明,陶虹杉,杨俊. 含混合项的拟线性Schrödinger方程的正规化基态解[J]. 数学物理学报, 2023, 43(4): 1062-1072.

Gui Kunming,Tao Hongshan,Yang Jun. Normalized Ground States for the Quasi-linear Schrödinger Equation with Combined Nonlinearities[J]. Acta mathematica scientia,Series A, 2023, 43(4): 1062-1072.

参考文献

[1]	Li H W, Zou W M. Quasilinear Schr?dinger equations: ground state and infinitely many normalized solutions. arXiv preprint, 2021, 2101.07574
[2]	Soave N. Normalized ground states for the NLS equation with combined nonlinearities. J Differ Equ, 2020, 269: 6941-6987
[3]	Borovskii A V, Galkin A L. Dynamical modulation of an ultrashort high-intensity laser pulse in matter. J Exp Theor Phys, 1993, 77(4): 562-573
[4]	Ritchie B. Relativistic self-focusing and channel formation in laser-plasma interactions. Phys Rev E, 1994, 50: 687-689
[5]	Hasse R W. A general method for the solution of nonlinear soliton and kink Schr?dinger equations. Z Phys B: Condens Matter, 1980, 37: 83-87
[6]	Shen Y T, Wang Y J. Soliton solutions for generalized quasilinear Schr?dinger equations. Nonlinear Anal Theory Methods Appl, 2013, 80: 194-201
[7]	Wang Y J, Shen Y T. Existence and asymptotic behavior of a class of quasilinear Schr?dinger equations. Adv Nonlinear Stud, 2018, 18(1): 131-150
[8]	Colin M, Jeanjean L, Squassina M. Stability and instability results for standing waves of quasi-linear Schr?dingerr equations. Adv Nonlinear Stud, 2010, 23(6): 1353-1385
[9]	Liu X Q, Liu J Q, Wang Z Q. Quasilinear elliptic equations with critical growth via perturbation method. J Differ Equ, 2013, 254(1): 102-124
[10]	Jeanjean L, Luo T J, Wang Z Q. Multiple normalized solutions for quasi-linear Schr?dingerr equations. J Differ Equ, 2015, 259(8): 3894-3928
[11]	Zeng X Y, Zhang Y M. Existence and asymptotic behavior for the ground state of quasilinear elliptic equations. Adv Nonlinear Stud, 2018, 18(4): 725-744
[12]	Lions P L. The concentration-compactness principle in the calculus of variations, the locally compact case, part 2. Ann I H Poincare-AN, 1984, 1(4): 223-283
[13]	Berestycki H, Lions P L. Nonlinear scalar field equations, II existence of infinitely many solutions. Arch Rat Mech AN, 1983, 82: 347-375