Exponential separation and principal Floquet bundles for linear parabolic equations on general bounded domains: divergence case
Juraj Húska · Indiana University Mathematics Journal · 2006
We consider linear nonautonomous second order parabolic equations on RN. 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 signchanging solutions are exponentially dominated by positive solutions.