含平均曲率算子的拟线性微分方程Dirichlet问题三个正解的存在性  

Existence of three positive solutions for Dirichlet problem of quasilinear differential equation with mean curvature operator

作　　者：何志乾 HE Zhi-qian(Teaching and Research Department of Basic Courses,Qinghai University,Xining 810016,Qinghai,China)

机构地区：[1]青海大学基础部,青海西宁810016

出　　处：《西北师范大学学报（自然科学版）》2022年第4期18-21,共4页Journal of Northwest Normal University(Natural Science)

基　　金：青海省自然科学基金资助项目(2021-ZJ-957Q);青海大学教育教学研究项目(JY202138)。

摘　　要：运用锥上的不动点指数理论,考虑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(u),x∈(0,1),u(0)=u(1)=0正解的存在性和多解性,其中λ>0为参数,f∈C([0,∞),[0,∞)).当f在原点处超线性增长,且在无穷远处次线性增长时,上述问题至少存在三个正解.By using the fixed point index theoery,the existence and multiplicity of positive solutions are discussed for Dirichlet problem of quasilinear differential equation with mean curvature operator-u′/1+(u′)2′=λf(u),x∈(0,1),u(0)=u(1)=0,whereλ>0 is parameter,f∈C([0,∞),[0,∞)).The existence of at least three positive solutions is proved for the problem when f has a suplinear behavior near the origin and sublinear behavior near infinity.

关 键 词：DIRICHLET问题 平均曲率算子 不动点指数 正解 多解性 欧式空间 

分 类 号：O175.8[理学—数学]