平面上一类非线性椭圆方程的最低能量解

doi:10.13438/j.cnki.jdzk.2019.01.004

吉首大学学报（自然科学版）

平面上一类非线性椭圆方程的最低能量解

王倩

(扬州大学数学科学学院，江苏扬州 225002)

出版日期:2019-01-25 发布日期:2019-01-26
作者简介:王倩（1992—），女，河南郑州人，扬州大学数学科学学院硕士生，主要从事偏微分方程研究.
基金资助:
国家自然科学基金面上资助项目（11571301）；国家青年科学基金资助项目（11301460）

Least Energy Solutions for a Class of Non-Linear Elliptic Equations on the Plane

WANG Qian

(School of Mathematical Science,Yangzhou University,Yangzhou 225002,Jiangsu China)

Online:2019-01-25 Published:2019-01-26

摘要/Abstract

摘要：

通过求条件极值的方法，证明了平面上的一类非线性椭圆方程有一个具有紧支撑集的最低能量解，这个解是球对称的且关于r=|x|单调递减.

关键词： 非线性椭圆方程, 最低能量解, 次线性, 紧支撑集

Abstract:

For a class of non-linear elliptic equations on the entire plane,constrained minimization method is used to prove that there exists a least energy solution which is compactly supported and spherically symmetric and decreases with respect to r=|x|.

Key words: semi-linear elliptic equation, least energy solution, sub-linear, compact support

王倩. 平面上一类非线性椭圆方程的最低能量解[J]. 吉首大学学报（自然科学版）, DOI: 10.13438/j.cnki.jdzk.2019.01.004.

WANG Qian. Least Energy Solutions for a Class of Non-Linear Elliptic Equations on the Plane[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.13438/j.cnki.jdzk.2019.01.004.

参考文献

[1] BERESTYCKI HENRI,LIONS PIERRE-LOUIS.Nonlinear Scalar Field Equations:I.Existence of a Ground State[J].Archive for Rational Mechanics and Analysis,1983,82(4):313-346.
[2] STRAUSS WALTER.Existence of Solitary Waves in Higher Dimensions[J].Communications in Mathematical Physics,1977,55(2):149-162.
[3] BERESTYCKI HENRI,GALLOUET THIERRY,KAVIAN OTARED.Equations de Champs Scalaires Euclidiens Nonlineaires dans le Plan[J].Comptes Rendus de l'Académie des Sciences.Série I.Mathématique,1983,297(5):307-310.
[4] BERESTYCKI HENRI,LIONS PIERRE-LOUIS.Nonlinear Scalar Field Equations:II.Existence of Infinitely Many Solutions[J].Archive for Rational Mechanics and Analysis,1983,82(4):347-375.
[5] BYEON JAEYOUNG,JEANJEAN LOUIS,MARIS MIHAI.Symmetry and Monotonicity of Least Energy Solutions[J].Calculus of Variations and Partial Differential Equations,2009,36(4):481-492.
[6] BREZIS HAIM,LIEB ELLIOTT.Minimum Action Solutions of Some Vector Field Equations[J].Communications in Mathematical Physics,1984,96(1):97-113.
[7] CORTZAR CARMEN,ELGUETA MANUEL,FELMER PATRICIO.On a Semilinear Elliptic Problem in RN with a Non-Lipschitzian Nonlinearity[J].Advances in Differential Equations,1996,1(2):199-218.
[8] GILBARG DAVID,TRUDINGER NEIL.Elliptic Partial Differential Equations of Eecond Order[M].New York:Springer Verlag,1977:219-255.
[9] HIRATA JUN,IKOMA NORIHISA,TANAKA KAZUNAGA.Nonlinear Scalar Field Equations in RN:Mountain Pass and Symmetric Mountain Pass Approaches[J].Topological Methods in Nonlinear Analysis,2010,35(2):253-276.
[10] LU QIUPING,LING ZHI.Least Energy Solutions for an Elliptic Problem Involving Sublinear Term and Peaking Phenomenon[J].Communications on Pure and Applied Analysis,2015,14(6):2 411-2 429.
[11] EDMUNDS DAVID ERIC,ILYIN ALEXEL A.Asymptotically Sharp Multiplicative Inequlities[J].Bulletin of the London Mathematical Society,1995,27(1):71-74.
[12] MOSER JURGEN.A Sharp Form of an Inequality by N.Trudinger[J].Indiana University Mathematics Journal,1971,20:1 077-1 092.
[13] TRUDING NEIL.On Embeddings into Orlicz Spaces and Some Applications[J].Journal of Applied Mathematics and Mechanics,1967,17(5):473-483.

平面上一类非线性椭圆方程的最低能量解

Least Energy Solutions for a Class of Non-Linear Elliptic Equations on the Plane

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	张申贵. 测度链上次线性二阶Hamilton系统周期解的存在性[J]. journal6, 2014, 35(5): 1-5.
[2]	张申贵. 一类次线性Hamilton系统的周期解[J]. journal6, 2014, 35(1): 4-7.
[3]	何小飞, 陈国平, 谢景力. 一类二阶非自治Hamilton系统的周期解[J]. journal6, 2010, 31(6): 14-18.