摘要
近年来,带有Hardy项和Hardy-Sobolev临界指数的奇异椭圆方程受到了广泛关注.根据奇异点所在区域的位置可以分为内部奇异(0∈Ω)和边界奇异(0∈■Ω)两种情况.边界奇异情况下,区域在原点处的曲率性质对方程解的存在性有着深刻的影响,对于低阶扰动的情形下椭圆方程解的存在性已有相应的结果.本文研究了在高阶扰动情形下具有边界奇异性的椭圆方程,利用山路引理、强极大值原理和一些分析技巧,证明了其正解的存在性,并且研究了边界的曲率性质及有关参数对方程解的存在性的影响.
In recent years,singular elliptic equations with Hardy term and Hardy-Sobolev critical exponent have been widely concerned.According to the location of the domain where the singular points are located,they can be divided into two cases:internal singular(0∈Ω)and boundary singular(0∈■Ω).In case of boundary singularity,the curvature property of the domain at the origin has a profound influence to the existence of the solution.In addition,under the condition of low order perturbation,the existence of the solution of elliptic equation has some corresponding results.In this paper,the elliptic equations have been studied with boundary singularity in the case of high order perturbation.By means of Mountain pass lemma,strong maximum principle and some analysis techniques,the existence of positive solution for this equation has been obtained.And,the influence of the existence of the solutions by the curvature properties of the boundary and the corresponding parameters been studied.
作者
贾润杰
商彦英
JIA Run-jie;SHANG Yan-ying(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)
出处
《西南师范大学学报（自然科学版）》
CAS
2021年第6期36-41,共6页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11971393).
