Existence and stability of multiple-spot solutions for the Gray-Scott model in \(\mathbb{R}^2\) (Q1858117)

In the present paper, the authors study the Gray-Scott model in a bounded domain \(\Omega\subset \mathbb{R}^2\). First they rigorously construct multiple interior spot solutions and then they prove results on the stability of such solutions. To this end the authors essentially use the Green function and its derivatives together with two nonlocal eigenvalue problems. Moreover they present a threshold behaviour for the stability.