带位势的基尔霍夫方程规范解的存在性

作     者：梁艳霞 LIANG Yan-xia

作者机构：School of Mathematics and StatisticsGuangdong University of TechnologyGuangzhou 510520China 

出 版 物：《Chinese Quarterly Journal of Mathematics》 (数学季刊（英文版）)

年 卷 期：2023年第38卷第2期

页      面：196-209页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Kirchhoff equation Normalized solutions Variational method 

摘      要：In this paper we discuss the following Kirchhoff equation(−a+b R _(R3)|∇u|^(2) dx
∆u+V(x)u+λu=µ|u|^(q−2)u+|u|^(p−2)u in R^(3),R R^(3) u^(2) dx=c^(2),where a,b,µ and c are positive numbers,λis unknown and appears as a Lagrange multiplier,143qp6 and V is a continuous non-positive function vanishing at *** some mild assumptions on V,we prove the existence of a mountain pass normalized *** we study the existence of normalized solution to mass supercritical Kirchhoff equation with potential via the minimax principle and Nehari-Pohozaev manifold.