含Caffarelli-Kohn-Nirenberg不等式和非线性边界条件的拟线性椭圆型方程组的多解性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1634-1645.

含Caffarelli-Kohn-Nirenberg不等式和非线性边界条件的拟线性椭圆型方程组的多解性

李琴¹(),杨作东^2,*()

¹ 安徽财经大学统计与应用数学学院安徽蚌埠 233030
² 南京信息工程大学教师教育学院南京 210044

收稿日期:2019-08-12 出版日期:2020-12-26 发布日期:2020-12-29
通讯作者: 杨作东 E-mail:liqin_math@163.com;zdyang_jin@263.net
作者简介:李琴, E-mail: liqin_math@163.com
基金资助:
安徽省自然科学基金青年项目(1808085QA15);安徽财经大学科学研究一般项目(ACKYC19050);国家自然科学基金(11571093)

Multiple Positive Solutions for a Quasilinear Elliptic System Involving the Caffarelli-Kohn-Nirenberg Inequality and Nonlinear Boundary Conditions

Qin Li¹(),Zuodong Yang^2,*()

¹ School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Anhui Bengbu 233030
² School of Teacher Education, Nanjing University of Information Science and Technology, Nanjing 210044

Received:2019-08-12 Online:2020-12-26 Published:2020-12-29
Contact: Zuodong Yang E-mail:liqin_math@163.com;zdyang_jin@263.net
Supported by:
the Anhui Natural Science Foundation(1808085QA15);the Scientific Research Project of Anhui University of Finance and Economics(ACKYC19050);the NSFC(11571093)

摘要/Abstract

摘要：

该文主要研究了一类含有Caffarelli-Kohn-Nirenberg不等式和非线性边界条件的拟线性椭圆型方程组, 利用变分法, 证明了至少两个正解的存在性.

关键词: 拟线性椭圆型方程组, Caffarelli-Kohn-Nirenberg不等式, 非线性边界条件, Nehari流形

Abstract:

This paper is concerned with a quasilinear elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and nonlinear boundary conditions. By means of variational methods, the existence of at least two positive solutions is obtained.

Key words: Quasilinear elliptic system, Caffarelli-Kohn-Nirenberg inequality, Nonlinear boundary conditions, Nehari manifold

中图分类号:

O175.2

李琴,杨作东. 含Caffarelli-Kohn-Nirenberg不等式和非线性边界条件的拟线性椭圆型方程组的多解性[J]. 数学物理学报, 2020, 40(6): 1634-1645.

Qin Li,Zuodong Yang. Multiple Positive Solutions for a Quasilinear Elliptic System Involving the Caffarelli-Kohn-Nirenberg Inequality and Nonlinear Boundary Conditions[J]. Acta mathematica scientia,Series A, 2020, 40(6): 1634-1645.

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