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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.08260 |
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Table of Contents:
- In this article, our main concern is to study the existence of bound and ground state solutions for the following fractional system of Schrödinger equations with Hardy potentials: \begin{equation*} \left\{ \begin{aligned} (-Δ)^{s_{1}} u - λ_{1} \frac{u~~}{|x|^{2s_{1}}} - u^{2_{s_{1}}^{*}-1} = ναh(x) u^{α-1}v^β & \quad \mbox{in} ~ \mathbb{R}^{N}, (-Δ)^{s_{2}} v - λ_{2} \frac{v~~}{|x|^{2s_{2}}} - v^{2_{s_{2}}^{*}-1} = νβh(x) u^αv^{β-1} & \quad \mbox{in} ~ \mathbb{R}^{N}, u,v >0 \quad \mbox{in} ~ \mathbb{R}^{N} \setminus \{0\}, \end{aligned} \right. \end{equation*} where $s_{1},s_{2} \in (0,1)~\text{and}~λ_{i}\in (0, Λ_{N,s_{i}})$ with $Λ_{N,s_{i}} = 2 π^{N/2} \frac{Γ^{2}(\frac{N+2s_i}{4}) Γ(\frac{N+2s_i}{2})}{Γ^{2}(\frac{N-2s_i}{4}) ~|Γ(-s_{i})|}, (i=1,2)$. By imposing certain assumptions on the parameters and on the function h, we obtain ground-state solutions using the concentration-compactness principle and the mountain-pass theorem.