SEPARATION STRUCTURE OF RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY

被引:3
作者
Bae, Soohyun [1 ]
Naito, Yuki [2 ]
机构
[1] Hanbat Natl Univ, Dept Math Sci, Daejeon 34158, South Korea
[2] Ehime Univ, Dept Math, Matsuyama, Ehime 7908577, Japan
基金
新加坡国家研究基金会;
关键词
Semilinear elliptic equations; exponential nonlinearity; separation; partial separation; critical dimension; R-N; CAUCHY-PROBLEM; HEAT-EQUATION; STEADY-STATES; STABILITY;
D O I
10.3934/dcds.2018198
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the semilinear elliptic equation Delta u + K(vertical bar x vertical bar)e(u) = 0 in R-N for N > 2, and investigate separation phenomena of radial solutions. In terms of intersection and separation, we classify the solution structures and establish characterizations of the structures. These observations lead to sufficient conditions for partial separation. For N = 10 + 4l with l > -2, the equation changes its nature drastically according to the sign of the derivative of r(-l) K(r) when r(-l) K(r) is monotonic in r and r(-l) K(r) -> 1 as r -> infinity.
引用
收藏
页码:4537 / 4554
页数:18
相关论文
共 18 条
[1]   Infinite multiplicity and separation structure of positive solutions for a semilinear elliptic equation in Rn [J].
Bae, S .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 200 (02) :274-311
[2]   Separation structure of positive radial solutions of a semilinear elliptic equation in Rn [J].
Bae, S .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 194 (02) :460-499
[3]   On a class of semilinear elliptic equations in Rn [J].
Bae, S ;
Chang, TK .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 185 (01) :225-250
[4]  
Bae S., P ROY SOC EDINBURG A
[5]   Entire solutions with asymptotic self-similarity for elliptic equations with exponential nonlinearity [J].
Bae, Soohyun .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 428 (02) :1085-1116
[6]   Existence and separation of positive radial solutions for semilinear elliptic equations [J].
Bae, Soohyun ;
Naito, Yuki .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (07) :2430-2463
[7]   ON THE STRUCTURE OF THE CONFORMAL GAUSSIAN CURVATURE EQUATION ON R2 [J].
CHENG, KS ;
NI, WM .
DUKE MATHEMATICAL JOURNAL, 1991, 62 (03) :721-737
[8]  
CHENG KS, 1987, T AM MATH SOC, V304, P639
[9]   ON THE ELLIPTIC EQUATION DELTA-U+KU(N+2)/(N-2)=0 AND RELATED TOPICS [J].
DING, WY ;
NI, WM .
DUKE MATHEMATICAL JOURNAL, 1985, 52 (02) :485-506
[10]   Further study on a nonlinear heat equation [J].
Gui, CF ;
Ni, WM ;
Wang, XF .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 169 (02) :588-613