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Infinite radial solutions for the fractional Kirchhoff equation

  • Lijuan ChenEmail author
  • Caisheng Chen
  • Hongwei Yang
  • Hongxue Song
Original Paper
  • 24 Downloads

Abstract

In this article, we are concerned with infinite radial solutions for the fractional Kirchhoff equation
$$\begin{aligned} M\left( \iint _{{\mathbb {R}}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+sp}}dxdy\right) (-\triangle )^{s}_{p}u+|u|^{p-2}u=f(u), \quad x\in {\mathbb {R}}^{N} \end{aligned}$$
where \(s\in (0,1)\) and \(f\in C({\mathbb {R}},{\mathbb {R}}^{+})\) without assuming the Ambrosetti–Rabinowitz condition. We obtain that the above equation has infinitely many radial solutions by variational methods under certain conditions.

Keywords

Fractional Kirchhoff equation Variational methods Symmetric mountain pass lemma 

Mathematics Subject Classification

35R11 35A15 35J60 

Notes

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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.College of ScienceHohai UniversityNanjingPeople’s Republic of China
  2. 2.Yancheng Institute of TechnologyYanchengPeople’s Republic of China
  3. 3.Shan Dong University of Science and TechnologyQingdaoPeople’s Republic of China
  4. 4.Nanjing University of Posts and TelecommunicationsNanjingPeople’s Republic of China

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