一类含平均曲率算子的拟线性微分方程Dirichlet问题3个正解的存在性  

Existence of 3 Positive Solutions for a Class of Dirichlet Problem of Quasilinear Differential Equation with Mean Curvature Operator

作　　者：苗亮英[1] 冯登娟 MIAO Liangying;FENG Dengjuan(School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China)

机构地区：[1]青海民族大学数学与统计学院,西宁810007

出　　处：《西南师范大学学报（自然科学版）》2022年第8期32-37,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：青海民族大学校级高层次人才基金项目(2021XJG10);国家自然科学基金项目(12061064).

摘　　要：利用锥上的不动点指数理论研究了欧氏空间中含平均曲率算子的拟线性微分方程Dirichlet问题-u′1+(u′)^(2)′=λf(x,u)x∈(0,1)u(0)=u(1)=0至少3个正解的存在性,其中λ>0为参数,f∈C([0,1]×[0,∞),[0,∞))并且f(x,s)>0,s>0,x∈[0,1].最后用一个例子验证了结果的正确性.In this paper,by means of the fixed point index theorem,we have studied the existence of at least 3 positive solutions for Dirichlet problem of quasilinear differential equation with mean curvature operator in Euclidean space-u′1+(u′)^(2)′=λf(x,u)x∈(0,1)u(0)=u(1)=0whereλ>0 is parameter,f∈C([0,1]×[0,∞),[0,∞))and f(x,s)>0,s>0,x∈[0,1].And,finally,an example has been given to verify the correctness of the main result.

关 键 词：平均曲率 不动点指数 正解 多解性 

分 类 号：O175.8[理学—数学]