Existence of solutions for critical Henon equations in hyperbolic spaces
In this article, we use variational methods to prove that for a suitable value of $lambda$, the problem $$displaylines{ -Delta_{mathbb{B}^N}u=(d(x))^{alpha}|u|^{2^{*}-2}u+lambda u, quad ugeq 0,quad uin H_0^1(Omega') }$$ possesses at least one non-trivial solution u as $alphao 0^+$, where...
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Texas State University
2013-01-01
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doaj-e71a5cbb78504400aee876369ea5e1092020-11-24T23:27:24ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-01-01201305,111Existence of solutions for critical Henon equations in hyperbolic spacesHaiyang HeJing QiuIn this article, we use variational methods to prove that for a suitable value of $lambda$, the problem $$displaylines{ -Delta_{mathbb{B}^N}u=(d(x))^{alpha}|u|^{2^{*}-2}u+lambda u, quad ugeq 0,quad uin H_0^1(Omega') }$$ possesses at least one non-trivial solution u as $alphao 0^+$, where $Omega'$ is a bounded domain in Hyperbolic space $mathbb{B}^N$, $d(x)=d_{mathbb{B}^N}(0,x)$. $Delta_{mathbb{B}^N}$ denotes the Laplace-Beltrami operator on $mathbb{B}^N$, $Ngeq 4$, $2^*=2N/(N-2)$. http://ejde.math.txstate.edu/Volumes/2013/05/abstr.htmlHenon equationsmountain pass theoremcritical growthhyperbolic space |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Haiyang He Jing Qiu |
spellingShingle |
Haiyang He Jing Qiu Existence of solutions for critical Henon equations in hyperbolic spaces Electronic Journal of Differential Equations Henon equations mountain pass theorem critical growth hyperbolic space |
author_facet |
Haiyang He Jing Qiu |
author_sort |
Haiyang He |
title |
Existence of solutions for critical Henon equations in hyperbolic spaces |
title_short |
Existence of solutions for critical Henon equations in hyperbolic spaces |
title_full |
Existence of solutions for critical Henon equations in hyperbolic spaces |
title_fullStr |
Existence of solutions for critical Henon equations in hyperbolic spaces |
title_full_unstemmed |
Existence of solutions for critical Henon equations in hyperbolic spaces |
title_sort |
existence of solutions for critical henon equations in hyperbolic spaces |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2013-01-01 |
description |
In this article, we use variational methods to prove that for a suitable value of $lambda$, the problem $$displaylines{ -Delta_{mathbb{B}^N}u=(d(x))^{alpha}|u|^{2^{*}-2}u+lambda u, quad ugeq 0,quad uin H_0^1(Omega') }$$ possesses at least one non-trivial solution u as $alphao 0^+$, where $Omega'$ is a bounded domain in Hyperbolic space $mathbb{B}^N$, $d(x)=d_{mathbb{B}^N}(0,x)$. $Delta_{mathbb{B}^N}$ denotes the Laplace-Beltrami operator on $mathbb{B}^N$, $Ngeq 4$, $2^*=2N/(N-2)$. |
topic |
Henon equations mountain pass theorem critical growth hyperbolic space |
url |
http://ejde.math.txstate.edu/Volumes/2013/05/abstr.html |
work_keys_str_mv |
AT haiyanghe existenceofsolutionsforcriticalhenonequationsinhyperbolicspaces AT jingqiu existenceofsolutionsforcriticalhenonequationsinhyperbolicspaces |
_version_ |
1725552118761259008 |