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Existence and multiplicity of positive solutions to fractional Laplacian systems with combined critical Sobolev terms

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Abstract

We deal with the existence and multiplicity of solutions for a non-local fractional system involving combined critical non-linearities. Some existence results are obtained by splitting the Nehari manifold and applying the Mountain–Pass theorem of Ambrosetti and Rabinowitz.

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Acknowledgements

The authors would like to thank the referees for their suggestions and helpful comments which improved the presentation of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Shahla Amiri & Abolfazl Behzadi

  2. Department of Mathematics, Faculty of Sciences, Razi University, 67149, Kermanshah, Iran

    Nemat Nyamoradi

  3. Dipartimento di Ingegneria industriale e Scienze Matematiche, Università Politecnica delle Marche, 60131, Ancona, Italy

    Vincenzo Ambrosio

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  1. Shahla Amiri
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  2. Nemat Nyamoradi
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  3. Abolfazl Behzadi
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  4. Vincenzo Ambrosio
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Correspondence to Nemat Nyamoradi.

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Amiri, S., Nyamoradi, N., Behzadi, A. et al. Existence and multiplicity of positive solutions to fractional Laplacian systems with combined critical Sobolev terms. Positivity 25, 1373–1402 (2021). https://doi.org/10.1007/s11117-021-00822-9

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  • DOI: https://doi.org/10.1007/s11117-021-00822-9

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