一类带Hardy项和Sobolev临界指数的椭圆型方程正解的存在性  

The Existence of a Positive Solution for an Elliptical Equation with Hardy Terms and Sobolev Critical Exponents

作　　者：李卫 王炜 李泽俊 赵秀娟 万优艳[1] 

机构地区：[1]江汉大学人工智能学院,湖北 武汉

出　　处：《理论数学》2024年第10期14-18,共5页Pure Mathematics

摘　　要：本文研究了一类带Hardy项和Sobolev临界指数的椭圆型方程。通过变分法,我们得到了方程的能量泛函在零点附近存在局部极小值点,且该极小值点为方程的正解。此外,当方程的扰动项趋于零时,该正解也趋于零。The elliptical equation with Hardy terms and Sobolev critical exponents is studied. By the variational methods, we have obtained that there exists a local minimum point of the energy functional related to the equation which is near zero, and the local minimum point is a positive solution of this equation. Moreover, this positive solution tends to zero when the perturbed term goes to zero.

关 键 词：变分方法 Hardy项 SOBOLEV临界指数 正解 扰动项 

分 类 号：O17[理学—数学]