摘要: 本文研究如下分数阶Kirchhoff-SchrÖdinger-Poisson系统
![](https://image.hanspub.org/IMAGE/Edit_e3873d1b-ce19-4b92-a0bb-0020ce418cc2.png)
,
非平凡解的存在性, 其中 a, b > 0 ,
![](https://image.hanspub.org/IMAGE/Edit_90fb70c2-9b0c-43f5-b548-434a23d1fafe.png)
, s, t ∈ (0, 1) 且 4s + 2t > 3, W (x) ∈ C(R
3) 变号且 lim
|x|→∞ W (x) = W
∞ < 0 ,
![](https://image.hanspub.org/IMAGE/Edit_232c87e9-7011-4f98-a894-d00122f4c3ed.png)
. 应用山路引理, 本文得到该系统至少存在一个非平凡解.
Abstract:
In this paper, we study the existence of nontrivial solution for fractional Kirchhoff- Schr
Ödinger-Poisson system:
![](https://image.hanspub.org/IMAGE/Edit_4fde5281-8932-4d55-ad44-ddd9fb11467e.png)
,
where a, b > 0,
![](https://image.hanspub.org/IMAGE/Edit_1c7bf283-eddd-4018-926b-c34e0f60bbb4.png)
, s, t ∈ (0, 1) and 4s + 2t > 3, W (x) ∈ C(R
3) is a sign-changing function with lim
|x|→∞ W (x) = W
∞ < 0,
![](https://image.hanspub.org/IMAGE/Edit_6e4ff66c-ab48-4900-8983-abce3f3974b8.png)
. By using mountain pass lemma, we obtain that this system has at least one nontrivial solution.