Total positivity and spectral properties of linearized operators

Abstract

For a class of semilinear elliptic equations, we establish criteria that guarantee that the linearized operator associated with a solution satisfies certain spectral assumptions that are widely used in the analysis of the stability of solitary waves. The criteria only involve the symbol of the linear operator and positivity and symmetry of the solution, and can therefore be verified without an explicit formula for the solution.

19 pages, 6 figures