Exact solution structures on some nonlocal overdetermined problems

Kazuki Sato; Futoshi Takahashi

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arXiv · 2512.14987

Exact solution structures on some nonlocal overdetermined problems

Kazuki Sato·Futoshi Takahashi

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Abstract

In this paper, we study the solution structures of Serrin-type overdetermined problems with Kirchhoff-type nonlocal terms. We prove that the exact number of solutions is the same as those of some transcendental equations defined by the nonlocal terms. We also obtain the explicit form of solutions by using the unique solutions of the overdetermined problems without the nonlocal terms.

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Kazuki Sato, Futoshi Takahashi. 2025-12-17. Exact solution structures on some nonlocal overdetermined problems. https://arxiv.org/abs/2512.14987

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