一类分数阶预定曲率问题多泡解的存在性  

Existence of Multi-bubbling Solutions for a Class of Fractional Prescribed Curvature Problems

作　　者：赵安澜 聂建军 An Lan ZHAO;Jian Jun NIE(School of Mathematics and Physics,North China Electric Power University,Beijing 102206,P.R.China)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《数学学报（中文版）》2024年第5期895-910,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12261031,12261076);中央高校基本科研费(2023MS078)。

摘　　要：我们考虑以下分数阶算子预定曲率问题:(-△)^(s)u=K(y)u^(2*s^(-1)),其中N≥3,0s*=2N/N-2s是分数阶临界Sobolev指数,K(y)是一正函数.当K(y)有一列模趋于正无穷大的局部极大值点的条件下,我们利用有限维约化方法,证明了上述问题任意有限个多泡解的存在性.这些解集中在K(y)的k个不同局部极大值点处.We consider the following prescribed curvature problem of fractional operator:(-△)^(s)u=K(y)u^(2*s^(-1)),where N≥3,0s*=2N/N-2s is the fractional critical Sobolev exponent,K(y)is a positive function.When K(y)has a sequence of strictly local maximum points moving to infinity,we use the finite dimensional reduction method to prove the existence of any finitely many multi-bubbling solutions to the above problem.These solutions concentrate at k different local maximum points of K(y).

关 键 词：临界指数 多泡解 能量泛函 有限维约化 

分 类 号：O175[理学—数学]