Existence and Asymptotic Behavior of Solutions for Hénon Equations in Hyperbolic Spaces
نویسندگان
چکیده
In this article, we consider the existence and asymptotic behavior of solutions for the Hénon equation −∆BN u = (d(x)) α|u|p−2u, x ∈ Ω u = 0 x ∈ ∂Ω, where ∆BN denotes the Laplace Beltrami operator on the disc model of the Hyperbolic space BN , d(x) = dBN (0, x), Ω ⊂ BN is geodesic ball with radius 1, α > 0, N ≥ 3. We study the existence of hyperbolic symmetric solutions when 2 < p < 2N+2α N−2 . We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent 2∗ = 2N N−2 with N ≥ 3.
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Existence and Asymptotic Behavior of Solutions for Hénon Type Equations
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