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arXiv · 2603.18732

Neumann problem with a discontinuous nonlinearity

Debajyoti Choudhuri·Dušan D. Repovš·Kamel Saoudi
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Abstract

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive an estimate that proves the well-posedness of the problem. This estimate serves as an evidence for the uniqueness of the existing solution when the boundary term is ``smooth".

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Debajyoti Choudhuri, Dušan D. Repovš, Kamel Saoudi. 2026-03-19. Neumann problem with a discontinuous nonlinearity. https://doi.org/10.1515/dema-2025-0229

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