Asymptotic Behavior of Least Energy Solutions for a Fractional Laplacian Eigenvalue Problem on Double-struck capital RN

被引：4

作者：

Wang, Yun Bo ^{[1
]}

Zeng, Xiao Yu ^{[2
]}

Zhou, Huan Song ^{[2
]}

机构：

[1] Northwest Univ, Ctr Nonlinear Studies, Sch Math, Xian 710127, Peoples R China

[2] Wuhan Univ Technol, Ctr Math Sci, Wuhan 430070, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2023年 / 39卷 / 04期

关键词：

Fractional Laplacian; eigenvalue problem; constrained variational problem; energy estimates; CONCENTRATION-COMPACTNESS PRINCIPLE; MASS CONCENTRATION; GROUND-STATES; UNIQUENESS; CALCULUS;

D O I：

10.1007/s10114-023-1074-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are interested in the existence and asymptotic behavior for the least energy solutions of the following fractional eigenvalue problem (P) (-.)su + V (x)u = mu u + am(x)|u| 4s N u, RN |u|2 dx = 1, u. H s (RN), where s. (0, 1), mu. R, a > 0, V (x) and m(x) are L8 (RN) functions with N = 2. We prove that there is a threshold a* s > 0 such that problem (P) has a least energy solution ua(x) for each a. (0, a* s) and ua blows up, as a a* s, at some point x0. RN, which makes V (x0) be the minimum and m(x0) be the maximum. Moreover, the precise blowup rates for ua are obtained under suitable conditions on V (x) and m(

引用

页码：707 / 727

页数：21

共 50 条

[41] Positive radial solutions of critical Henon equations on the unit ball in Double-struck capital RN$$ {\mathbb{R}}∧N $$
Wang, Cong
Su, Jiabao
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (17) : 11769 - 11806
[42] The Ground State Solutions for Kirchhoff-Schrodinger Type Equations with Singular Exponential Nonlinearities in Double-struck capital RN
Liu, Yanjun
Liu, Chungen
CHINESE ANNALS OF MATHEMATICS SERIES B, 2022, 43 (04) : 549 - 566
[43] Lower bound for the perimeter density at singular points of a minimizing cluster in Double-struck capital RN☆
Hirsch, Jonas
Marini, Michele
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2020, 26
[44] Analytical and numerical applications for the Fourier multiplier operators on Double-struck capital Rn x (0, ∞)
Soltani, Fethi
Nemri, Akram
APPLICABLE ANALYSIS, 2015, 94 (08) : 1545 - 1560
[45] On the Fourier orthonormal bases of a class of self-similar measures on Double-struck capital Rn
Tang, Wei
Wang, Zhi-Yong
FORUM MATHEMATICUM, 2023, 35 (06) : 1667 - 1684
[46] Lp Decay Rate for a Nonlinear Convection Diffusion Reaction Equation in Double-struck capital Rn
Liu, Guo-wei
Xu, Hong-mei
Xia, Yuan-mei
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2021, 37 (02): : 380 - 392
[47] Fractional nonuniform multiresolution analysis in L2(Double-struck capital R)
Srivastava, Hari M.
Shah, Firdous A.
Lone, Waseem Z.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (11) : 9351 - 9372
[48] On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space Double-struck capital Rn
Shirokov, Dmitry
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2020, 27 (02) : 199 - 218
[49] Qualitative analysis of solutions to a nonlocal Choquard-Kirchhoff diffusion equations in Double-struck capital RN$$ {\mathbb{R}}∧N $$
Li, Lijuan
Zhou, Jun
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (03) : 3255 - 3284
[50] On the behavior of least energy solutions of a fractional (p, q(p))-Laplacian problem as p goes to infinity
Ercole, Grey
Medeiros, Aldo H. S.
Pereira, Gilberto A.
ASYMPTOTIC ANALYSIS, 2021, 123 (3-4) : 237 - 262

← 1 2 3 4 5 →