Stability of equilibrium solutions of a double power reaction diffusion equation with a Dirac interaction

Abstract

In this paper we provide detailed information about the instability of equilibrium solutions of a nonlinear family of localized reaction-difussion equations in dimensione one. Beyond we provide explicit formulas to the equilibrium solutions, via perturbation method and we calculate the exact number of positive eigenvalues of the linear operator associated to the stability problem, which allow us to compute the dimension of the unstable manifold.