Kazuki Sato, Futoshi Takahashi
Abstract:
In this article, we study the solution structures of Serrin-type over-determined
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
over-determined problems without the nonlocal terms.
Submitted January 11, 2026. Published April 6, 2026.
Math Subject Classifications: 34C23, 37G99.
Key Words: Over-determined problems; Kirchhoff-type; nonlocal term.
DOI: 10.58997/ejde.2026.26
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Kazuki Sato Department of Mathematics Osaka Metropolitan University 3-3-138, Sumiyoshi-ku Sugimoto-cho, Osaka, Japan email: sf22817a@st.omu.ac.jp |
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Futoshi Takahashi Department of Mathematics Osaka Metropolitan University 3-3-138, Sumiyoshi-ku Sugimoto-cho, Osaka, Japan email: futoshi@omu.ac.jp |
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