Generalized Choquard Equations Driven by Nonhomogeneous Operators
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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.
KeywordsChoquard equation variational methods nonlinear elliptic equation Hardy–Littlewood–Sobolev inequality
Mathematics Subject Classification35A15 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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