Quasilinear Fractional Neumann Problems

Dimitri Mugnai () and Edoardo Proietti Lippi
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Dimitri Mugnai: Department of Ecological and Biological Sciences, University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy
Edoardo Proietti Lippi: Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

Mathematics, 2024, vol. 13, issue 1, 1-24

Abstract: We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, even in the linear case, for which no regularity can indeed be assumed.

Keywords: mixed local and fractional p -Laplacians; Neumann boundary conditions; regularity; superlinear problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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