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.

引用

页数：13

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