Existence of nontrivial solutions for fractional Schrodinger equations with critical or supercritical growth
Existence of nontrivial solutions for fractional Schrodinger equations with critical or supercritical growth
复制标题
具有临界或超临界增长的分数阶薛定谔方程非平凡解的存在性
DOI：
10.1002/mma.5441
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发表时间：
2019
影响因子：
2.9
通讯作者：
Wang Wenbo
中科院分区：
文献类型：
--
作者：
Li Quanqing;Teng Kaimin;Wu Xian;Wang Wenbo
本文研究了具有临界或超临界增长的分数阶Schrödinger方程，其中0 <s< 1，N> 2s,λ> 0,,,（−Δ）表示阶的分数阶拉普拉斯函数，f是一个连续的超线性次临界函数。在适当的条件下，用变分方法证明了该方程对smallλ>有非平凡解。我们的主要贡献与我们能够处理这个案件有关。
In this paper, we study the following fractional Schrödinger equation with critical or supercritical growth where 0 <s< 1,N> 2s,λ> 0, , , ( − Δ)sdenotes the fractional Laplacian of ordersandfis a continuous superlinear but subcritical function. Under some suitable conditions, we prove that the equation has a nontrivial solution for smallλ> 0 by variational methods. Our main contribution is related to the fact that we are able to deal with the case .