Solution structure of nonlocal Serrin-type over-determined problems

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. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/26/abstr.html