含一般非线性项Kirchhoff型约束变分问题Schwarz对称极小解的存在性  

Existence of Schwarz symmetric minimizers for a Kirchhoff constrained variational problem with general nonlinear term

作　　者：张贻民 杨华华 Zhang Yimin;Yang Huahua(Center for Mathematical Sciences,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学数学科学研究中心,武汉430070

出　　处：《河南师范大学学报（自然科学版）》2021年第3期9-17,F0002,共10页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11771127);中央高校基本科研业务费专项基金资助(WUT:2020IB011,2020IB017,2020IB019).

摘　　要：利用约束变分理论和对称递减重排技巧考虑一般非线性项情形下一类Kirchhoff型约束变分问题Schwarz对称极小解的存在性和不存在性.针对非线性项的指数和约束∫R^(N)|u|^(2)dx=c^(2)中的c与极小化问题Schwarz对称极小解存在与否的关系,得到了一个细致明确的划分.In this paper,by using the theory of constrained variational and symmetric decreasing rearrangement technique,the existence and nonexistence of Schwarz symmetric minimizers of a class of Kirchhoff constrained variational problem with a general nonlinear term were considered.Especially,a complete classification of the existence and nonexistence for Schwarz symmetric minimizers with respect to the exponent in nonlinear term and c in manifold ∫R^(N)|u|^(2)dx=c^(2) was obtained.

关 键 词：Schwarz对称极小解 递减重排 Kirchhoff约束变分 

分 类 号：O175.25[理学—数学]