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Existence and nonexistence of solutions to nonlocal elliptic problems

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Abstract

It is established existence and nonexistence of solutions to nonlocal elliptic problems involving the generalized pseudo-relativistic Hartree equation. Our arguments are based on variational methods together with a fine analysis on the Pohozaev identity.

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Acknowledgements

The authors would like to thank Aldo H. S. Medeiros for many useful conversations and suggestions.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, 31270-901, Brazil

    Hamilton Bueno & Gilberto A. Pereira

  2. Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, GO, 74001-970, Brazil

    Edcarlos D. Silva

  3. Departamento de Matemática, Universidade de Brasília, Brasília, DF, 70910-900, Brazil

    Ricardo Ruviaro

Authors
  1. Hamilton Bueno
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  2. Gilberto A. Pereira
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  3. Edcarlos D. Silva
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  4. Ricardo Ruviaro
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Additional information

This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

Research supported in part by INCTmat/MCT/Brazil, CNPq and CAPES/Brazil. The third author was partially supported by CNPq with Grants 309026/2020-2 and 429955/2018-9.

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Bueno, H., Pereira, G.A., Silva, E.D. et al. Existence and nonexistence of solutions to nonlocal elliptic problems. Partial Differ. Equ. Appl. 3, 8 (2022). https://doi.org/10.1007/s42985-021-00142-3

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