Generalized Choquard Equations Driven by Nonhomogeneous Operators

  • Claudianor O. Alves
  • Vicenţiu D. RădulescuEmail author
  • Leandro S. Tavares
Open Access


In this work we prove the existence of solutions for a class of generalized Choquard equations involving the \(\Delta _\Phi \)-Laplacian operator. Our arguments are essentially based on variational methods. One of the main difficulties in this approach is to use the Hardy–Littlewood–Sobolev inequality for nonlinearities involving N-functions. The methods developed in this paper can be extended to wide classes of nonlinear problems driven by nonhomogeneous operators.


Choquard equation variational methods nonlinear elliptic equation Hardy–Littlewood–Sobolev inequality 

Mathematics Subject Classification

35A15 35J62 35J60 



This work started when Leandro S. Tavares was visiting the Federal University of Campina Grande. He thanks the hospitality of Professor Claudianor Alves and of the other members of the department. V. D. Rădulescu was supported by the Slovenian Research Agency grants P1-0292, J1-8131, J1-7025, N1-0064, and N1-0083. He also acknowledges the support through the Project MTM2017-85449-P of the DGISPI (Spain). C. O. Alves was partially supported by CNPq/Brazil 301807/2013-2.


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Authors and Affiliations

  1. 1.Unidade Acadêmica de MatemáticaUniversidade Federal de Campina GrandeCampina GrandeBrazil
  2. 2.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland
  3. 3.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  4. 4.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  5. 5.Centro de Ciências e TecnologiaUniversidade Federal do CaririJuazeiro do NorteBrazil

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