Semilinear elliptic equations of the Henon-type in hyperbolic space

被引：3
|
作者：
Carriao, P. C. [1 ]
Faria, L. F. O. [2 ]
Miyagaki, O. H. [2 ]
机构：
[1] Rua Souza Naves 3600, BR-85801120 Cascavel, PR, Brazil
[2] Univ Fed Juiz de Fora, Dept Matemat, BR-36036330 Juiz de Fora, MG, Brazil
来源：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2016年 / 18卷 / 02期
关键词：
Henon problem; hyperbolic space; Sobolev with weights; positive solutions; POSITIVE SOLUTIONS; GROUND-STATES; EXISTENCE;
D O I：
10.1142/S0219199715500261
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a class of the semilinear elliptic equations of the Henon-type in hyperbolic space. The problem involves a logarithm weight in the Poincare ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former Ni result made for a unit ball in R-N. Combining this compactness embedding with the Mountain Pass Theorem, a result of the existence of positive solution is established.
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页数：13
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