Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
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发表时间：
2012-02
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通讯作者：
S. Dipierro;Giampiero Palatucci;E. Valdinoci
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作者：
S. Dipierro;Giampiero Palatucci;E. Valdinoci
本文讨论 \mathbb{R}^N 中的以下一类非局部薛定谔方程 (-\Delta)^s u + u = |u|^{p-1}u ，对于 s\in (0,1)。我们证明分数 Sobolev 空间 H^s(\mathbb{R}^N) 中解 $u$ 的存在性和对称性结果。我们的结果与经典局部对应物（即 s=1 时）的结果明显一致。
This paper deals with the following class of nonlocal Schrodinger equations (-\Delta)^s u + u = |u|^{p-1}u in \mathbb{R}^N, for s\in (0,1). We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space H^s(\mathbb{R}^N). Our results are in clear accordance with those for the classical local counterpart, that is when s=1.