Blow-Up Behavior of L2-Norm Solutions for Kirchhoff Equation in a Bounded Domain

被引：0

作者：

Zhu, Xincai ^{[1
]}

Zhang, Shu ^{[2
]}

Wang, Changjian ^{[1
]}

He, Chunxia ^{[1
]}

机构：

[1] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Henan, Peoples R China

[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2023年 / 46卷 / 05期

关键词：

Kirchhoff equation; L-2-norm solution; Minimizer; Bounded domain; Blow-up behavior; Regularity; POSITIVE SOLUTIONS; SCHRODINGER-EQUATIONS; NORMALIZED SOLUTIONS; EXISTENCE; UNIQUENESS; STATES; MASS;

D O I：

10.1007/s40840-023-01548-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to studying the following Kirchhoff equation - (a + b integral(Omega) vertical bar del u vertical bar(2)dx) Delta u = mu u + beta vertical bar u vertical bar(p)u + lambda vertical bar u vertical bar(q)u, x is an element of Omega u = 0, x is an element of partial derivative Omega, where Omega subset of R-3 is a bounded connected domain and integral(Omega) |u|(2)dx = 1. The results of existence and nonexistence on L-2-norm solutions are given. Our argument shows that the blow-up behavior of L-2-norm solution occurs, and the mass concentrates at an inner point of L-2, or the neighborhood of some boundary point.

引用

页数：14

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