一类拟线性薛定谔方程的多解性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 93-100.

一类拟线性薛定谔方程的多解性

薛艳昉^*(),朱新才()

信阳师范学院数学与统计学院河南信阳 464000

收稿日期:2021-05-13 修回日期:2022-07-25 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*薛艳昉, E-mail: xueyanfang2015@163.com
作者简介:朱新才, E-mail: zhuxc68@163.com
基金资助:
国家自然科学基金(11901499);国家自然科学基金(11901500);信阳师范学院南湖学者青年项目(201912)

Existence of Multiple Solutions for a Class of Quasilinear Schrödinger Equations

Xue Yanfang^*(),Zhu Xincai()

College of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000

Received:2021-05-13 Revised:2022-07-25 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(11901499);The NSFC(11901500);Nanhu Scholar Program for Young Scholars of XYNU(201912)

摘要/Abstract

摘要：

该文研究了强制位势下拟线性薛定谔方程的多解性问题. 首先利用变量代换, 将拟线性方程转化成半线性方程, 然后借助喷泉定理, 得到了该方程的无穷多个高能量解.

关键词: 拟线性薛定谔方程, 喷泉定理, 强制位势

Abstract:

The multiple solutions are studied for a class of Quasilinear Schr?dinger equation under the coercive potential. By using the method of variable substitution, the quasilinear problem is transformed into a semilinear one, then infinitely many high energy solutions of the equation are obtained with the help of the fountain theorem.

Key words: Quasilinear Schr?dinger equations, Fountain theorem, Coercive potential

中图分类号:

O177.91

薛艳昉, 朱新才. 一类拟线性薛定谔方程的多解性[J]. 数学物理学报, 2023, 43(1): 93-100.

Xue Yanfang, Zhu Xincai. Existence of Multiple Solutions for a Class of Quasilinear Schrödinger Equations[J]. Acta mathematica scientia,Series A, 2023, 43(1): 93-100.

参考文献

[1]	Chen X L, Sudan R N. Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse. Phys Review Letters, 1993, 70: 2082-2085
[2]	Chu C M, Liu H D. Existence of positive solutions for a quasilinear Schr?dinger equation. Nonlinear Anal, 2018, 44: 118-127
[3]	Hasse R W. A general method for the solution of nonlinear soliton and kink Schr?dinger equations. Zeitschrift für Physik B Condensed Matter, 1980, 37: 83-87
[4]	Huang W T, Xiang J L. Soliton solutions for a quasilinear Schr?dinger equation with critical exponent. Commun Pure Appl Anal, 2016, 15(4): 1309-1333
[5]	Jalilian Y. Infinitely many solutions for a class of quasilinear Schr?dinger equations involving sign-changing weight functions. Applicable Analysis, 2019, 98(7): 1347-1366
[6]	Kosevich A M, Ivanov B A, Kovalev A S. Magnetic solitons. Physics Reports, 1990, 194: 117-238
[7]	Kurihura S. Large-amplitude quasi-solitons in superfluid films. J Phys Soc Japan, 1981, 50: 3262-3267
[8]	Li G B. Positive solution for quasilinear Schr?dinger equations with a parameter. Commun Pure Appl Anal, 2015, 14(5): 1803-1816
[9]	Liu J Q, Wang Y Q, Wang Z Q. Soliton solutions for quasilinear Schr?dinger equations, II. J Differential Equations, 2003, 187(2): 473-493
[10]	Makhankov V G, Fedyanin V K. Non-linear effects in quasi-one-dimensional models of condensed matter theory. Physics Reports, 1984, 104: 1-86
[11]	梅艳芳, 王友军. 一类非线性Schr?dinger方程三种类型的解. 数学物理学报, 2019, 39A(5): 1087-1093
[11]	Mei Y F, Wang Y J. Three types of solutions for a class of nonlinear Schr?dinger equations. Acta Math Sci, 2019, 39A(5): 1087-1093
[12]	Shang T T, Liang R X. Ground state solutions for a quasilinear elliptic equation with general critical nonlinearity. Complex Var Ell Equ, 2021, 66(4): 586-613
[13]	Shen Y T, Wang Y J. Soliton solutions for generalized quasilinear Schr?dinger equations. Nonlinear Anal, 2013, 80: 194-201
[14]	Shen Y T, Wang Y J. Standing waves for a class of quasilinear Schr?dinger equations. Complex Var Ell Equ, 2016, 61(6): 817-842
[15]	Willem M. Minimax Theorems. Boston: Birkh?user, 1996
[16]	Wu X. Multiple solutions for quasilinear Schr?dinger equations with a parameter. J Differential Equations, 2014, 256(7): 2619-2632
[17]	徐家发. 具有半正非线性项的分数阶差分方程组边值问题的正解. 数学物理学报, 2020, 40A(1): 134-147
[17]	Xu J F. Positive solutions of boundary value problems for fractional difference equations with semipositive nonlinearity. Acta Math Sci, 2020, 40A(1): 134-147
[18]	Zhang J, Tang X H, Zhang W. Infinitely many solutions of quasilinear Schr?dinger equation with sign-changing potential. J Math Anal Appl, 2014, 420(2): 1762-1775