On the existence of two stationary solutions for a free boundary problem describing cell motility

Abstract

This paper is concerned with the existence of stationary solutions for a free boundary problem related to cell motility. In recent years, the author and Ninomiya \cite{monobe_ninomiya} showed that there exist at least two stationary solutions with disk-shaped domains in isotropic boundary conditions. In this paper, it will be shown that there exist exactly two stationary solutions for the free boundary problem under the same boundary conditions. The proof is based on the weak maximum principle and the mean-valued theorem.