Infinitely many solutions for a Hénon-type system in hyperbolic space.

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2020
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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.
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Hénon equation, Variational methods
Citação
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: <https://advancesindifferenceequations.springeropen.com/articles/10.1186/s13662-019-2469-6>. Acesso em: 03 jul. 2020.