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On the Existence of Solutions for an elliptic system of Equations with Arbitrary Order Growth

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 415-424页

作者： Zhong-yuan LIU Academy of Mathematics and systems Science Chinese Academy of Sciences

Let BR be the ball centered at the origin with radius R in RN （N≥2）. In this paper we study the existence of solution for the following elliptic systemwhere λ 〉 0,μ 〉 0 p ≥ 2, q ≥ 2, u is the unit outward normal at the boundary OBR. Under certain assumptions on K（｜x｜）, using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity.

关键词： elliptic system Nehari manifold variational method

Existence of Solutions for the Critical elliptic system with Inverse Square Potentials

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 315-328页

作者： Zhao-xia LIU Zhao-hui LIU Department of Information and Computational Science School of Sciences Minzu University of China Suncun Middle School Gaoxin District of Jinan

Let Ω∈← 0 be an open bounded domain in RN （N 〉 3） and 2＊（s） = 2（N-8） =2（N-s）N-22. We consider the following elliptic system of two equations in where A, μ 〉 0 and α, β 〉 1 satisfy α ＋ β = 2＊（s... 详细信息

Let Ω∈← 0 be an open bounded domain in RN （N 〉 3） and 2＊（s） = 2（N-8） =2（N-s）N-22. We consider the following elliptic system of two equations in where A, μ 〉 0 and α, β 〉 1 satisfy α ＋ β = 2＊（s）. Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions.

关键词： elliptic system variational functional Palais-Smale condition critical point

Positive Solutions to a Neumann Problem of Semilinear elliptic system with Critical Nonlinearity

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Acta Mathematicae Applicatae Sinica 2006年第4期22卷 687-702页

作者： Wei-hua Yang Academy of Mathematics and systems Science Chinese Academy of Science Beijing 100080 China

In this paper, we consider the Neumann boundary value problem for a system of two elliptic equations involving the critical Sobolev exponents. By means of blowing-up method, we obtain behavior of positives with low en... 详细信息

关键词： elliptic system Neumann problem critical Sobolev exponent

MULTIPLICITY OF POSITIVE SOLUTIONS FOR AN elliptic system

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Analysis in Theory and Applications 2003年第2期19卷 145-152页

作者： Han Zhaoxiu (ZheJiang University, China)Department of Mathematics Zhejiang University Hangzhou,Zhejiang,310028 P.R.China Zhejiang University Zhejiang China Department of Mathematics Zhejiang University Hangzhou Zhejiang 310028 China

By considering the properties of , we show the multiplicity of at least two positivesolutions of the elliptic system.

关键词： multiplicity elliptic system

Positive Entire Solutions to an elliptic system

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Northeastern Mathematical Journal 2001年第1期17卷 1-4页

作者：张中新王俊禹黄明游 InstituteofMathematics JilinUniversityChangchun130021 不详

In a recent paper [1], Ye has demonstrated that the singular nonlinear elliptic equation has a positive entire solution under some conditions imposed on f. Problems of finding positive entire solutions to elliptic equations have been studied by many authors since they have certain physical backgrounds and practical applications. For details, see, for example, [ 1-3] and the references therein.

关键词： elliptic system positive entire solution existence

MULTIPLE SOLUTIONS OF SOME elliptic systemS WITH LINEAR COUPLINGS

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Acta Mathematica Scientia 2021年第4期41卷 1141-1150页

作者：陈宇彤苏加宝孙明正田如顺 School of Mathematical Sciences Capital Normal UniversityBeijing 100048China College of Sciences North China University of TechnologyBeijing 100144China

In this paper,we study the existence of nontrivial solutions to the elliptic system {-△u=λv+Fu(x,u,v),x∈Ω,-△v=λu+Fv(x,u,v),x∈Ω,u=v=0,x∈∂Ω,where Ω■R^(N) is bounded with a smooth *** the Morse theory and the... 详细信息

关键词： Morse theory multiplicity elliptic system linear couplings

ON THE NONLINEAR RIEMANN PROBLEMS FOR GENERALFIRST elliptic systemS IN THE PLANE

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Applied Mathematics and Mechanics(English Edition) 2005年第1期26卷 79-84页

作者：李明忠宋洁 Department of Mathematics Shanghai University Shanghai 200444 P.R.China Department of Mathematics East China University of Science and TechnologyShanghai 200237 P.R.China

The nonlinear Riemann problem for general systems of the first-order linear and quasi-linear equations in the plane are *** translates them to singular integral equations and proves the existence of the solution by me... 详细信息

关键词： Riemann problem elliptic system singular integral equation

MULTIPLICITY OF POSITIVE SOLUTIONS FOR SINGULAR elliptic systemS WITH CRITICAL SOBOLEV-HARDY AND CONCAVE EXPONENTS

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Acta Mathematica Scientia 2011年第3期31卷 791-804页

作者： Tsing-San Hsu Huei-Lin Li Center for General Education Chang Gung University

In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded *** means of variational methods,the multiplicity of positive solutions to this... 详细信息

关键词： elliptic system critical Sobolev-Hardy exponent concave exponents Nehari manifold

EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR elliptic systemS IN R^N WITH ZERO MASS

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Acta Mathematica Scientia 2013年第4期33卷 913-928页

作者：李工宝叶红雨 School of Mathematics and Statistics Central China Normal University

In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.

关键词： existence positive solutions elliptic system linking geometric structure zero mass case