WOLFF TYPE POTENTIAL ESTIMATES AND APPLICATION TO NONLINEAR EQUATIONS WITH NEGATIVE EXPONENTS

被引：3
作者：
Lei, Yutian [1 ]
机构：
[1] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 05期
关键词：
Wolff potential; conformal geometry; gamma-Laplace equation; k-Hessian equation; asymptotic behavior; INVARIANT INTEGRAL-EQUATIONS; POSITIVE SOLUTIONS; CLASSIFICATION; THEOREMS; SYSTEMS;
D O I：
10.3934/dcds.2015.35.2067
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are concerned with the positive continuous entire solutions of the Wolff type integral equation u(x) = c(x) W beta,gamma(u(-p))(x), u > 0 in R-n, where n >= 1, p > 0, gamma > 1, beta > 0 and beta gamma not equal n. In addition, c(x) is a double bounded function. Such an integral equation is related to the study of the conformal geometry and nonlinear PDEs, such as gamma-Laplace equations and k-Hessian equations with negative exponents. By some Wolff type potential integral estimates, we obtain the asymptotic rates and the integrability of positive solutions, and discuss the existence and nonexistence results of the radial solutions.
引用
收藏
页码：2067 / 2078
页数：12
相关论文
共 29 条
[1]   Wolff's inequality for radially nonincreasing kernels and applications to trace inequalities [J].
Cascante, C ;
Ortega, JM ;
Verbitsky, IE .
POTENTIAL ANALYSIS, 2002, 16 (04) :347-372
[2]   THE PROPERTIES OF POSITIVE SOLUTIONS TO AN INTEGRAL SYSTEM INVOLVING WOLFF POTENTIAL [J].
Chen, Huan ;
Lu, Zhongxue .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (05) :1879-1904
[3]   RADIAL SYMMETRY OF SOLUTIONS FOR SOME INTEGRAL SYSTEMS OF WOLFF TYPE [J].
Chen, Wenxiong ;
Li, Congming .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 30 (04) :1083-1093
[4]   CLASSIFICATION OF SOLUTIONS OF SOME NONLINEAR ELLIPTIC-EQUATIONS [J].
CHEN, WX ;
LI, CM .
DUKE MATHEMATICAL JOURNAL, 1991, 63 (03) :615-622
[5]   Classification of solutions for an integral equation [J].
Chen, WX ;
Li, CM ;
Ou, B .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2006, 59 (03) :330-343
[6]   Nonlinear biharmonic equations with negative exponents [J].
Choi, Y. S. ;
Xu, Xingwang .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (01) :216-234
[7]   GLOBAL AND LOCAL BEHAVIOR OF POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS [J].
GIDAS, B ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1981, 34 (04) :525-598
[8]   LIOUVILLE TYPE RESULTS AND REGULARITY OF THE EXTREMAL SOLUTIONS OF BIHARMONIC EQUATION WITH NEGATIVE EXPONENTS [J].
Guo, Zongming ;
Wei, Juncheng .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (06) :2561-2580
[9]   THIN SETS IN NONLINEAR POTENTIAL-THEORY [J].
HEDBERG, LI ;
WOLFF, TH .
ANNALES DE L INSTITUT FOURIER, 1983, 33 (04) :161-187
[10]   STRUCTURE THEOREMS FOR POSITIVE RADIAL SOLUTIONS TO DIV(VERTICAL-BAR-DU-VERTICAL-BAR(M)-2DU)+K(VERTICAL-BAR-X-VERTICAL-BAR)U(Q)=0 IN R(N) [J].
KAWANO, N ;
YANAGIDA, E ;
YOTSUTANI, S .
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1993, 45 (04) :719-742
123