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  

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

作　　者：李琴[1] 杨作东 Li Qin;Yang Zuodong(School of Statistics and Applied Mathematics,Anhui University of Finance and Economics,Anhui Bengbu 233030;School of Teacher Education,Nanjing University of Information Science and Technology,Nanjing 210044)

机构地区：[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

出　　处：《数学物理学报（A辑）》2020年第6期1634-1645,共12页Acta Mathematica Scientia

基　　金：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)。

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.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.

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 

分 类 号：O175.2[理学—数学]