Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a super-spherical sector

被引：1

作者：

Yao, Ruofei ^{[1
,2
]}

Chen, Hongbin ^{[3
]}

Gui, Changfeng ^{[4
]}

机构：

[1] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China

[2] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China

[3] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

[4] Univ Texas San Antonio, Dept Math, San Antonio, TX 78249 USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 60卷 / 04期

关键词：

Primary; 35J61; Secondary; 35B06; 35M12; 35B50; LEAST-ENERGY SOLUTIONS; MULTI-PEAK SOLUTIONS; MAXIMUM PRINCIPLE; LAYER SOLUTIONS; MONOTONICITY; INTERIOR;

D O I：

10.1007/s00526-021-01999-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we establish some symmetry results for positive solutions of semilinear elliptic equations with mixed boundary conditions. In particular, we show that the positive solution in a super-spherical sector must be symmetric. The monotonicity property is also proved. Our proof is based on the well-known moving plane methods.

引用

页数：25

共 50 条

[21] Existence of multiple solutions for nonlinear elliptic equations with mixed boundary conditions
Xie, ZQ
Xiao, HJ
ACTA MATHEMATICA SCIENTIA, 2001, 21 (01) : 61 - 68
[22] Symmetry properties for positive solutions to some elliptic equations in sector domains with large amplitude
Zhu, MJ
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 261 (02) : 733 - 740
[23] Positive Solutions to Nonlinear Elliptic Equations Depending on a Parameter with Dirichlet Boundary Conditions
Seshadev Padhi
John R. Graef
Ankur Kanaujiya
Differential Equations and Dynamical Systems, 2023, 31 : 319 - 336
[24] On the existence of positive solutions of singular nonlinear elliptic equations with Dirichlet boundary conditions
Hirata, Kentaro
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) : 885 - 891
[25] UNIQUENESS OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS
Hai, D. D.
Shivaji, Ratnasingham
Wang, Xiao
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2025, 24 (02) : 255 - 263
[26] Positive Solutions to Nonlinear Elliptic Equations Depending on a Parameter with Dirichlet Boundary Conditions
Padhi, Seshadev
Graef, John R.
Kanaujiya, Ankur
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2023, 31 (02) : 319 - 336
[27] POSITIVE RADIAL SOLUTIONS FOR ELLIPTIC EQUATIONS ON EXTERIOR DOMAINS WITH NONLINEAR BOUNDARY CONDITIONS
Butler, Dagny
Ko, Eunkyung
Lee, Eun Kyoung
Shivaji, R.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (06) : 2713 - 2731
[28] BIFURCATION PHENOMENA FOR THE POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC PROBLEMS WITH MIXED BOUNDARY CONDITIONS
Barletta, G.
Livrea, R.
Papageorgiou, N. S.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2016, 17 (08) : 1497 - 1516
[29] Radial symmetry of positive solutions of nonlinear elliptic equations
Taliaferro, SD
JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (02) : 219 - 253
[30] EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO ELLIPTIC PROBLEMS WITH SUBLINEAR MIXED BOUNDARY CONDITIONS
Garcia-Melian, Jorge
Rossi, Julio D.
Sabina De Lis, Jose C.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2009, 11 (04) : 585 - 613

← 1 2 3 4 5 →