2025/12/17 by Sato, Kazuki, Takahashi, Futoshi
Mathematics · #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Fixed Point Theorems Analysis
paper · doi:10.48550/arxiv.2512.14987
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.