Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations  

作　　者：Yu-ting KANG Peng LUO Chang-lin XIANG Xue-xiu ZHONG 

机构地区：[1]Department of Mathematics,College of Mathematics and Physics,China Three Gorges University,Yichang 443002,China [2]School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,China [3]Three Gorges Mathematical Research Center,China Three Gorges University,Yichang 443002,China [4]South China Research Center for Applied Mathematics and Interdisciplinary Studies,South China Normal University,Guangzhou 510631,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期414-424,共11页应用数学学报(英文版)

基　　金：partially supported by National Natural Science Foundation of China(Nos.12171183,11831009);the Fundamental Research Funds for the Central Universities(Nos.KJ02072020-0319,CCNU22LJ002);financially supported by National Natural Science Foundation of China(No.12271296);partially supported by National Natural Science Foundation of China(No.11801581);Guangdong Basic and Applied Basic Research Foundation(2021A1515010034);Guangzhou Basic and Applied Basic Research Foundation(202102020225);Province Natural Science Fund of Guangdong(2018A030310082).

摘　　要：In the present paper,we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations-M(∫_(R^(N))|∇_(v)|^(2)dx)Δ^(v)=g(v)in R^(N);where M:[0;+∞)→R is a continuous function satisfying some suitable conditions and v∈H^(1)(R^(N)).Applying our results to the case M(t)=at+b,a;b>0,we make it clear all the positive solutions for all dimensions N≥1.Our results can be viewed as a generalization of the corresponding results of Li et al.

关 键 词：Kirchhoff type equations general nonlinearities UNIQUENESS NONDEGENERACY singular perturbation problem 

分 类 号：O175.25[理学—数学]