The existence of solutions for Hénon equation in hyperbolic space

He, Haiyang

doi:10.3792/pjaa.89.24

Cited by 7 publications

(10 citation statements)

References 11 publications

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“…More precisely, she explored the Strauss radial estimate for hyperbolic space together with the mountain pass theorem. In a subsequent paper [2], He and Qiu proved the existence of at least one non-trivial positive solution for the critical Hénon equation…”

Section: Introduction and The Main Resultsmentioning

confidence: 98%

“…has attracted attention. Unlike the corresponding problem in the Euclidean space R N , He in [1] proved the existence of a positive solution to the above problem over the range p ∈ (2, 2N+2α N-2 ) in the hyperbolic space. More precisely, she explored the Strauss radial estimate for hyperbolic space together with the mountain pass theorem.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…where B N is the Poincaré ball model for the hyperbolic space, H 1 r (B N ) denotes the Sobolev space of a radial H 1 We assume the following hypotheses on K and Q:…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…It is easy to see that u n u and v n v in H 1 r (B N ). We will use the same calculus used by Haiyang He [1] (page 26). We want to show that…”

Section: Preliminariesmentioning

confidence: 99%

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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: 98%

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…where B N is the Poincaré ball model for the hyperbolic space, H 1 r (B N ) denotes the Sobolev space of a radial H 1 We assume the following hypotheses on K and Q:…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…It is easy to see that u n u and v n v in H 1 r (B N ). We will use the same calculus used by Haiyang He [1] (page 26). We want to show that…”

Section: Preliminariesmentioning

confidence: 99%

See 2 more Smart Citations

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

Cunha

Lemos

2020

Adv Differ Equ

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“…In [5], the classification of radial solutions of problem (1.7) was done by Bonforte etc. In [14], He applied the variational methods to study the following problem…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

He¹

2015

Ann. Acad. Sci. Fenn. Math.

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Semilinear elliptic equations of the Hénon-type in hyperbolic space

Carrião

Faria

Miyagaki

2016

Commun. Contemp. Math.

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This paper deals with a class of the semilinear elliptic equations of the Hénon-type in hyperbolic space. The problem involves a logarithm weight in the Poincaré ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former Ni result made for a unit ball in [Formula: see text] Combining this compactness embedding with the Mountain Pass Theorem, a result of the existence of positive solution is established.

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The existence of solutions for Hénon equation in hyperbolic space

Cited by 7 publications

References 11 publications

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

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

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

Semilinear elliptic equations of the Hénon-type in hyperbolic space

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