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Nonlinear Choquard equations on hyperbolic space

He Haiyang

Opuscula Mathematica

2022

Vol. 42, no. 5

691--708

In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation [formula] on the hyperbolic space BN, where ΔBN denotes the Laplace-Beltrami operator on BN, [formula] λ is a real parameter, 0 < μ < N, 1 < p ≤ 2∗μ,N ≥ 3 and [formula] is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.

Ground states of coupled critical Choquard equations with weighted potentials

Zhu Gaili, Duan Chunping, Zhang Jianjun, Zhang Huixing

Opuscula Mathematica

2022

Vol. 42, no. 2

337--354

In this paper, we are concerned with the following coupled Choquard type system with weighted potentials [formula] where N ≥ 3, μ1, μ2, β > 0 and V1(x), V2(x) are nonnegative functions. Via the variational approach, one positive ground state solution of this system is obtained under some certain assumptions on V1(x), V2(x) and Q(x). Moreover, by using Hardy’s inequality and one Pohozǎev identity, a non-existence result of non-trivial solutions is also considered.