Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension

Gabriel Neves Cunha, Francesca Faraci () and Kaye Silva
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Gabriel Neves Cunha: Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia 74001-970, Brazil
Francesca Faraci: Department of Mathematics and Computer Sciences, University of Catania, 95125 Catania, Italy
Kaye Silva: Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia 74001-970, Brazil

Mathematics, 2024, vol. 12, issue 18, 1-13

Abstract: In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point.

Keywords: strong singularity; critical nonlinearity; non-local operator; subcritical perturbation; topology of sublevels; Szulkin functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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