Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 969-983

INFINITELY MANY SOLUTIONS FOR HARDY-HÉNON TYPE ELLIPTIC SYSTEM IN HYPERBOLIC SPACE

Haiyang He

Hunan Normal University, College of Mathematics and Computer Science
Changsha, Hunan 410081, P.R. China; hehy917 'at' hotmail.com

Abstract. In this paper, we investigate the existence results for Hardy-Hénon type strongly indefinite elliptic system

(0.1)
-Δ_HNu = (d_b(x))^α|v|^p-1v,
-Δ_HNv = (d_b(x))^β|v|^q-1u,

in the whole hyperbolic space H^N, where α,β ∈ R, N > 4, d_b(x) = d_HN(b,x), and b is a fixed point in hyperbolic space. We prove that there exist infinitely many nontrivial radial solutions for problem (0.1) under some suitable conditions.

2010 Mathematics Subject Classification: Primary 58J05, 35J60.

Key words: Hardy-Hénon type system, strongly indefinite, hyperbolic space.

Reference to this article: H. He: Infinitely many solutions for Hardy-Hénon type elliptic system in hyperbolic space. Ann. Acad. Sci. Fenn. Math. 40 (2015), 969-983.

Full document as PDF file

doi:10.5186/aasfm.2015.4056

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