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A Hardy–Littlewood–Sobolev-Type Inequality for Variable Exponents and Applications to Quasilinear Choquard Equations Involving Variable Exponent

  • Claudianor O. Alves
  • Leandro S. TavaresEmail author
Article
  • 58 Downloads

Abstract

In this work, we have proved a Hardy–Littlewood–Sobolev inequality for variable exponents. After that, we use this inequality together with the variational method to establish the existence of solution for a class of Choquard equations involving the p(x)-Laplacian operator.

Keywords

Variational methods quasilinear elliptic equations nonlinear elliptic equations Choquard equation 

Mathematics Subject Classification

35A15 35J62 35J60 

Notes

Acknowledgements

This work was done while the second author was visiting the Federal University of Campina Grande. He thanks the hospitality of professor Claudianor Alves and of the other members of the department. The authors warmly thank the anonymous referee for his/her useful and nice comments on the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Unidade Acadêmica de MatemáticaUniversidade Federal de Campina GrandeCampina GrandeBrazil

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