半线性退化椭圆方程解的奇异性与退化性

Abstract

CLC Number:

O175

Dongyan Li,Yan Dong. Singularity and Decay of Solutions for a Degenerate Semilinear Elliptic Equation[J].Acta mathematica scientia,Series A, 2019, 39(6): 1376-1380.

Trendmd

References 8

1	Gidas B , Spruck J . Global and local behavior of positive solutions of nonlinear elliptic equations. Comm Pure Appl Math, 1981, 34 (4): 525- 598 doi: 10.1002/cpa.3160340406
2	Gidas B , Spruck J . A priori bounds for positive solutions of nonlinear elliptic equations. Comm Partial Differential Equations, 1981, 6 (8): 883- 901 doi: 10.1080/03605308108820196
3	Du Y H , Guo Z M . Finite Morse index solutions of weighted elliptic equations and the critical exponents. Calc Var Partial Dif, 2015, 54: 3161- 3181 doi: 10.1007/s00526-015-0897-z
4	Guo Z M , Guan X H , Wan F S . Sobolev type embedding and weak solutions with a prescribed singular set. Sci China Math, 2016, 50: 1975- 1994
5	Guo Z M , Mei L F , Wan F S , et al. Embedding of weighted Sobolev spaces and degenerate elliptic problems. Sci China Math, 2017, 60: 1399- 1418 doi: 10.1007/s11425-016-0403-6
6	Guo Z M , Wan F S . Further study of a weighted elliptic equation. Sci China Math, 2017, 60 (12): 2391- 2406 doi: 10.1007/s11425-017-9134-7
7	Guo Z M , Zhou F . Sub-harmonicity, monotonicity formula and finite Morse index solutions of an elliptic with negative exponent. Sci China Math, 2015, 58: 2301- 2316 doi: 10.1007/s11425-015-4988-2
8	Poláčik P , Quittner P , Souplet P . Singularity and decay estimates in superlinear problems via Liouville-type theorems, Ⅰ:Elliptic equations and systems. Duke Math J, 2007, 139 (3): 555- 579 doi: 10.1215/S0012-7094-07-13935-8

[1]	Wang Hanyi, Huang Shiyu, Xiang Jianlin. Mountain-pass Solution and Ground State Solution for a Kirchhoff Type Elliptic Equation [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1041-1057.
[2]	Shou Xiaohua, Zhong Xin. A Serrin Criterion for Three-Dimensional Compressible Non-Isothermal Nematic Liquid Crystal Flows [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1058-1076.
[3]	Zhu Weipeng, Li Jinlu, Wu Xing. Global Smooth Solutions of the Damped Boussinesq Equations with a Class of Large Initial Data [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1077-1085.
[4]	Zuo Wenwen, Zhou Shouming. Global Solutions for the Parabolic-Parabolic Keller-Segel Equation with a Logistic Source Term in High Dimensions [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1100-1109.
[5]	Sun Zexin, Zhang Li, Bao Xiongxiong. Spreading Speeds for Partially Degenerate Models in Multi-Dimensional Time-Space Periodic Media [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1110-1127.
[6]	Tu Kun, Ding Huisheng. Shadowing Properties of Semilinear Nonautonomous Evolution Equations on Banach Spaces [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1144-1160.
[7]	Lv Dongting. Globally Asymptotic Stability of 2-Species Reaction-Diffusion Systems of Spatially Inhomogeneous Models [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1171-1183.
[8]	Zeng Xiaping, Lu Wenwen, Pang Guoping, Liang Zhiqing. Single Population Dynamics Model of Fish with Seasonal Switching and Impulsive Perturbations [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1206-1216.
[9]	Liu Yu, Chen Guanggan, Li Shuyong. Nonlinear Stability of Traveling Waves for Stochastic Kuramoto-Sivashinsky Equation [J]. Acta mathematica scientia,Series A, 2025, 45(3): 790-806.
[10]	Fu Huijie, Xu Meizhen. $J$-Self-Adjointness and Green's Function of Discontinuous Second-Order Differential Operator with Eigenparameters in the Boundary Conditions [J]. Acta mathematica scientia,Series A, 2025, 45(3): 707-725.
[11]	Feng Zhendong, Guo Fei, Li Yuequn. Breakdown of Solutions to a Weakly Coupled System of Semilinear Wave Equations [J]. Acta mathematica scientia,Series A, 2025, 45(3): 726-747.
[12]	Lu Gaojie, Han Zhong, Liu Lu. Darboux Transformation and Exact Solutions of the Nonlocal Reverse Space-Time Higher-Order Nonlinear Schrödinger Equation [J]. Acta mathematica scientia,Series A, 2025, 45(3): 767-775.
[13]	Wu Peng, Zhang Shuai, Fang Cheng. Dynamics of an Age-Space Structure Pine Wilt Disease Model with Nonlocal Diffusion and Spatial Heterogeneity [J]. Acta mathematica scientia,Series A, 2025, 45(3): 946-959.
[14]	Li Qian, Xing Yanyuan. Finite Time Blow up of Solutions for Nonlinear Wave Equation with the Damping Term at Arbitrarily Positive Initial Energy [J]. Acta mathematica scientia,Series A, 2025, 45(3): 748-755.
[15]	Zheng Yanping, Shen Jianhe. Traveling Fronts in a Social Tension-Outbursts Multi-Scale Reaction-Diffusion Equation with Allee Effect [J]. Acta mathematica scientia,Series A, 2025, 45(3): 776-789.

Singularity and Decay of Solutions for a Degenerate Semilinear Elliptic Equation

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 8

Related Articles 15

Metrics

Comments

Recommended 10