含分数阶p-Laplacian算子基尔霍夫方程解的存在性及其渐近行为  

Existence and Asymptotic Behavior of Solutions for Kirchhoff Equations Involving the Fractional p-Laplacian

作　　者：孟笑莹 陆璐 Meng Xiaoying;Lu Lu(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073

出　　处：《数学物理学报(A辑)》2025年第2期434-449,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(11771127)。

摘　　要：该文主要考虑一类含分数阶p-Laplacian算子基尔霍夫型方程正规化解的存在性和渐近行为.利用能量估计技巧,当q∈(p,p+2sp^(2)/N)时,该文得到了含分数阶p-Laplacian算子基尔霍夫型方程正规化解的存在性与非线性项指数q和预定值c(其中∫_(R^(N))|u|^(p)dx=c^(p))的一个完整的分类.当q≥p+2sp^(2)/N时,该文得到了方程山路型正规化解的存在性.进一步探讨了正规化解关于c的渐近行为.In this paper,we are interested in the existence of normalized solutions for some fractional Kirchhoff equations with p-Laplacian operator:For the existence and nonexistence of normalized solutions,using the method of energy estimates,we give a complete classification with respect to nonlinear term exponent q and an explicit threshold value of c(with∫_(R^(N))|u|^(p)dx=c^(p))in the range q∈(p,p+2sp^(2)/N).We also derive some existence of mountain pass type normalized solutions on the L^(2)manifold in the range q≥p+2sp^(2)/N.Furthermore,some asymptotic behaviors with respect to c were also given.

关 键 词：基尔霍夫方程 正规化解 存在性 渐近行为 

分 类 号：O175.25[理学—数学]