NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS  

作　　者：Wenmin LIU Xuexiu ZHONG Jinfang ZHOU 刘文民;钟学秀;周锦芳(School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China;South China Research Center for Applied Mathematics and Interdisciplinary Studies&School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China)

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China [2]South China Research Center for Applied Mathematics and Interdisciplinary Studies&School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China

出　　处：《Acta Mathematica Scientia》2024年第5期1886-1902,共17页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(12271184);the Guangzhou Basic and Applied Basic Research Foundation(2024A04J10001).

摘　　要：In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

关 键 词：normalized solution Kirchhoff type equations general nonlinearities asymptotic behavior 

分 类 号：O175[理学—数学]