Cunha, Patrícia Leal daLemos, Flávio Almeida2020-08-172020-08-172020CUNHA, P. L. da; LEMOS, F. A. Infinitely many solutions for a Hénon-type system in hyperbolic space. Advances in Difference Equations, v. 2020, n. 29, jan. 2020. Disponível em: <https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-019-2469-6>. Acesso em: 03 jul. 2020.1687-1847http://www.repositorio.ufop.br/handle/123456789/12609This paper is devoted to studying the semilinear elliptic system of Hénon type ⎧⎩⎨⎪⎪−ΔBNu=K(d(x))Qu(u,v),−ΔBNv=K(d(x))Qv(u,v),u,v∈H1r(BN),N≥3,{−ΔBNu=K(d(x))Qu(u,v),−ΔBNv=K(d(x))Qv(u,v),u,v∈Hr1(BN),N≥3, in the hyperbolic space BNBN, where H1r(BN)={u∈H1(BN):u is radial}Hr1(BN)={u∈H1(BN):u is radial} and −ΔBN−ΔBN denotes the Laplace–Beltrami operator on BNBN, d(x)=dBN(0,x)d(x)=dBN(0,x), Q∈C1(R×R,R)Q∈C1(R×R,R) is p-homogeneous, and K≥0K≥0 is a continuous function. We prove a compactness result and, together with Clark’s theorem, we establish the existence of infinitely many solutions.en-USabertoHénon equationVariational methodsArtigo publicado em periodicoThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Fonte: o próprio artigo.https://doi.org/10.1186/s13662-019-2469-6