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Title: Infinitely many solutions for a Hénon-type system in hyperbolic space.
Authors: Cunha, Patrícia Leal da
Lemos, Flávio Almeida
Keywords: Hénon equation
Variational methods
Issue Date: 2020
Citation: CUNHA, 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: <>. Acesso em: 03 jul. 2020.
Abstract: This 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.
ISSN: 1687-1847
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