Infinitely many solutions for Hardy-Hénon type elliptic system in hyperbolic space

He, Hongchao

doi:10.5186/aasfm.2015.4056

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Cited by 4 publications

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“…provided that α → 0 + and for a suitable value of λ, where Ω is a bounded domain in hyperbolic space B N . Finally, by working in the whole hyperbolic space H N , He [3] considered the following Hardy-Hénon type system:…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

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

Cunha

Lemos

2020

Adv Differ Equ

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This paper is devoted to studying the semilinear elliptic system of Hénon type ⎧ ⎪ ⎨ ⎪ ⎩-B N u = K(d(x))Q u (u, v),-B N v = K(d(x))Q v (u, v), u, v ∈ H 1 r (B N), N ≥ 3, in the hyperbolic space B N , where H 1 r (B N) = {u ∈ H 1 (B N) : u is radial} and-B N denotes the Laplace-Beltrami operator on B N , d(x) = d B N (0, x), Q ∈ C 1 (R × R, R) is p-homogeneous, and K ≥ 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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Section: Introduction and The Main Resultsmentioning

confidence: 99%

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

Cunha

Lemos

2020

Adv Differ Equ

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show abstract

“…provided that α → 0 + and for a suitable value of λ, where Ω ′ is a bounded domain in hyperbolic space B N . Finally, by working in the hole hyperbolic space H N , He [12] considered the following Hardy-Hénon type system…”

Section: Introduction and Main Resultsmentioning

confidence: 99%