Exponential separation and principal Floquet bundles for linear parabolic equations on $R^N$

Abstract

We consider linear nonautonomous second order parabolic equations on $\R^N$. Under an instability condition, we prove the existence of two complementary Floquet bundles, one spanned by a positive entire solution - the principal Floquet bundle, the other one consisting of sign-changing solutions. We establish an exponential separation between the two bundles, showing in particular that a class of sign-changing solutions are exponentially dominated by positive solutions.