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

共 34 条

[1]

[Anonymous], 1996, Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications

[2]

[Anonymous], 2011, Courant Lecture Notes in Mathematics

[3] Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions [J].

Chems Eddine, Nabil ;

Ragusa, Maria Alessandra .

APPLICABLE ANALYSIS, 2022, 101 (11) :3958-3988

[4] Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in R3 [J].

Deng, Yinbin ;

Peng, Shuangjie ;

Shuai, Wei .

JOURNAL OF FUNCTIONAL ANALYSIS, 2015, 269 (11) :3500-3527

[5] EXISTENCE AND NON-EXISTENCE RESULTS FOR SEMILINEAR ELLIPTIC PROBLEMS IN UNBOUNDED-DOMAINS [J].

ESTEBAN, MJ ;

LIONS, PL .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1982, 93 :1-14

[6]

Gidas B., 1981, ADV MATH SUPPLEMEN A, V7A, P369

[7] Fractional calculus, zeta functions and Shannon entropy [J].

Guariglia, Emanuel .

OPEN MATHEMATICS, 2021, 19 (01) :87-100

[8]

Guariglia E, 2016, SPRINGER P MATH STAT, V179, P337, DOI 10.1007/978-3-319-42105-6_16

[9] BLOW-UP SOLUTIONS FOR A KIRCHHOFF TYPE ELLIPTIC EQUATION WITH TRAPPING POTENTIAL [J].

Guo, Helin ;

Zhang, Yimin ;

Zhou, Huansong .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (05) :1875-1897

[10] On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions [J].

Guo, Yujin ;

Seiringer, Robert .

LETTERS IN MATHEMATICAL PHYSICS, 2014, 104 (02) :141-156

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