Abstract
The objective of this article is to investigate the existence of a weak solution to a class of nonlocal-type problem with Neumann boundary condition, which involves a reaction term that relies on the gradient of the solution, and a multivalued term. Our approach is based on the topological degree theory for a class of weakly upper semi-continuous, locally bounded set-valued operators of (\(S_+\)) type. The novelty of our work lies in the fact that we are able to manage three major characteristics simultaneously: a convection term, a nonlocal operator and a discontinuous nonlinearity.
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Zineddaine, G., Sabiry, A., Melliani, S. et al. On a discontinuous nonlinear elliptic problem of nonlocal-type with Neumann boundary condition. J Elliptic Parabol Equ 10, 19–38 (2024). https://doi.org/10.1007/s41808-023-00248-2
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DOI: https://doi.org/10.1007/s41808-023-00248-2