On elliptic problems with Choquard term and singular nonlinearity

Article type: Research Article

Authors: Choudhuri, Debajyoti^a | Repovš, Dušan D.^{b; *} | Saoudi, Kamel^c

Affiliations: [a] Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, Odisha, India | [b] Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana & Institute of Mathematics, Physics and Mechanics, Ljubljana, 1000, Slovenia | [c] Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, Dammam 34212, Saudi Arabia

Correspondence: [*] Corresponding author. E-mail: dusan.repovs@guest.arnes.si.

Abstract: Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded a.e. in the domain Ω and is Hölder continuous.

Keywords: Choquard term, variational method, dual fountain theorem

DOI: 10.3233/ASY-221812

Journal: Asymptotic Analysis, vol. 133, no. 1-2, pp. 255-266, 2023