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Singular Doubly Nonlocal Elliptic Problems with Choquard Type Critical Growth Nonlinearities

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Abstract

The theory of elliptic equations involving singular nonlinearities is well-studied topic but the interaction of singular type nonlinearity with nonlocal nonlinearity in elliptic problems has not been investigated so far. In this article, we study the very singular and doubly nonlocal singular problem \((P_\lambda )\) (See below). Firstly, we establish a very weak comparison principle and the optimal Sobolev regularity. Next using the critical point theory of nonsmooth analysis and the geometry of the energy functional, we establish the global multiplicity of positive weak solutions.

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Acknowledgements

The authors would like to thank the anonymous referees for a careful reading and valuable comments.

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Authors and Affiliations

  1. Université de Pau et des Pays de l’Adour, LMAP (UMR E2S-UPPA CNRS 5142), Bat. IPRA, Avenue de l’Université, 64013, Pau, France

    Jacques Giacomoni

  2. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khaz, New Delhi, 110016, India

    Divya Goel & K. Sreenadh

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  1. Jacques Giacomoni
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  2. Divya Goel
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  3. K. Sreenadh
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Correspondence to Jacques Giacomoni.

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Giacomoni, J., Goel, D. & Sreenadh, K. Singular Doubly Nonlocal Elliptic Problems with Choquard Type Critical Growth Nonlinearities . J Geom Anal 31, 4492–4530 (2021). https://doi.org/10.1007/s12220-020-00441-y

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