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Existence of infinitely many solutions for fractional p-Laplacian Schrödinger–Kirchhoff type equations with sign-changing potential

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we investigate the existence of infinitely many solutions for the following fractional p-Laplacian equations of Schrödinger–Kirchhoff type

$$\begin{aligned} \left( a+b\iint _{{{\mathbb {R}}}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right) ^{p-1} (-\Delta )^s_p u+V(x)|u|^{p-2}u=f(x,u) \end{aligned}$$

in \({{\mathbb {R}}}^N\), where \(0<s<1\), \(2\le p<\infty \), \(a,b>0\) are constants. Under some appropriate assumptions on V and f, we prove that the above problem possesses multiple solutions by utilizing some new tricks. Furthermore, our assumptions are suitable and different from those studied previously.

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Acknowledgements

This work is partially supported by the NNSF (Nos. 11601145, 11571370), by the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2017zzts312), by the Natural Science Foundation of Hunan Provincial (No. 2017JJ3130), and by the Outstanding youth project of Education Department of Hunan Province (17B143).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Youpei Zhang & Xianhua Tang

  2. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, Hunan, People’s Republic of China

    Jian Zhang

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  1. Youpei Zhang
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Correspondence to Youpei Zhang.

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Zhang, Y., Tang, X. & Zhang, J. Existence of infinitely many solutions for fractional p-Laplacian Schrödinger–Kirchhoff type equations with sign-changing potential. RACSAM 113, 569–586 (2019). https://doi.org/10.1007/s13398-018-0497-9

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  • DOI: https://doi.org/10.1007/s13398-018-0497-9

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