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Nodal solutions for fractional Schrödinger-Poisson problems

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Abstract

In this paper, we consider the following fractional Schrödinger-Poisson problem,

$$\begin{cases}\epsilon^{2s}(-\Delta)^{s}u+V(x)u+\phi{u}=\mid{u}\mid^{p-1}u, & x\in\mathbb{R}^N,\\(-\Delta)^t\phi=u^2, & x\in\mathbb{R}^N,\end{cases}$$

where ε > 0 is a small parameter, N ⩾ 3 and V(x) is a potential function. We construct non-radial sign-changing solutions, whose components may have spikes clustering at the local minimum point of V(x).

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant Nos. 11501264 and 11871253), the Natural Science Foundation of Jiangxi Province (Grant No. 20171BCB23030) and Jiangxi Provincial Department of Education Fund. The second author was supported by National Natural Science Foundation of China (Grant Nos. 11671179 and 11771300).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China

    Wei Long, Jianfu Yang & Weilin Yu

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  1. Wei Long
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  2. Jianfu Yang
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  3. Weilin Yu
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Correspondence to Wei Long.

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Long, W., Yang, J. & Yu, W. Nodal solutions for fractional Schrödinger-Poisson problems. Sci. China Math. 63, 2267–2286 (2020). https://doi.org/10.1007/s11425-018-9452-y

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