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

Abstract

In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction‐diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.