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Infinitely Many Solutions for Fractional p-Kirchhoff Equations

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Abstract

In this paper we consider the existence of infinitely many weak solutions for fractional Schrödinger–Kirchhoff problems. Precisely speaking, we investigate

$$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad \mathrm{in}~\Omega ,\\ u=0, &{}\quad \mathrm{in}~\mathbb {R}^n\setminus \Omega , \end{array}\right. \end{aligned}$$

where \(\Omega \) is a bounded subset with Lipshcitz boundary \(\partial \Omega \), \(0<s<1\) is fixed, and \(1<p<n\), \((-\triangle )_p^s\) is the fractional p-Laplacian operator. Kirchhoff function M, potential function V and nonlinearity f satisfy some suitable assumptions. Under those conditions, some new multiplicity results are obtained by applying the fountain theorem and the dual fountain theorem.

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Authors and Affiliations

  1. College of Science, Hohai University, Nanjing, 210098, People’s Republic of China

    Libo Yang & Tianqing An

  2. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an, 223003, People’s Republic of China

    Libo Yang

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  1. Libo Yang
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Correspondence to Libo Yang.

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Supported by Natural Science Foundation of Huaiyin Institute of Technology (No. 17HGZ004).

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Yang, L., An, T. Infinitely Many Solutions for Fractional p-Kirchhoff Equations. Mediterr. J. Math. 15, 80 (2018). https://doi.org/10.1007/s00009-018-1124-x

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  • DOI: https://doi.org/10.1007/s00009-018-1124-x

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