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Radial solutions for a fractional Kirchhoff type equation in \(\mathbb {R}^N\)

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Abstract

This work is concerned with the following equation of Kirchhoff type involving the fractional Laplacian

$$\begin{aligned} \left( a+b\int _{\mathbb {R}^N}\left| (-\varDelta )^{\frac{s}{2}}u\right| ^2dx\right) (-\varDelta )^su+u=f(u) \, \text{ in } \mathbb {R}^N. \end{aligned}$$

By transforming this equation into an equivalent system, under suitable assumptions we establish the existence of at least two nontrivial radial solutions without (AR) condition. Moreover, the nonexistence of solutions is also investigated.

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Acknowledgements

The authors are grateful to the anonymous referee for the careful reading of the manuscript and for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, FTSH, Abdelmalek Essaadi University, Tétouan, Morocco

    Mohammed Massar

  2. CRMEF, Oujda, Morocco

    Mohamed Talbi

Authors
  1. Mohammed Massar
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  2. Mohamed Talbi
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Correspondence to Mohammed Massar.

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Communicated by K Sandeep.

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Massar, M., Talbi, M. Radial solutions for a fractional Kirchhoff type equation in \(\mathbb {R}^N\). Indian J Pure Appl Math 52, 897–902 (2021). https://doi.org/10.1007/s13226-021-00106-8

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  • DOI: https://doi.org/10.1007/s13226-021-00106-8

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