Abstract
In this paper, we study the following fractional Schrödinger equation
where \({N \geq 1, s \in (0,1)}\), \({a \in \mathbb{R}}\) and V(x) is a measurable function. We prove the existence or nonexistence of ground states for the above equation under \({L^{2}}\)-constraint and some assumptions on \({V(x)}\) and a. Besides, we also analyze the behavior of ground states as a tends to some fixed constant.
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The authors sincerely thank the anonymous reviewer’s professional comments and suggestions, which improves greatly the quality of this manuscript. The authors sincerely thank Professor Shuangjie Peng for helpful suggestions and discussions.
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He, Q., Long, W. The concentration of solutions to a fractional Schrödinger equation. Z. Angew. Math. Phys. 67, 9 (2016). https://doi.org/10.1007/s00033-015-0607-x
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DOI: https://doi.org/10.1007/s00033-015-0607-x