# American Institute of Mathematical Sciences

January  2008, 20(1): 81-113. doi: 10.3934/dcds.2008.20.81

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

 1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received  January 2007 Revised  June 2007 Published  October 2007

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.
Citation: J. Húska, Peter Poláčik. Exponential separation and principal Floquet bundles for linear parabolic equations on $R^N$. Discrete & Continuous Dynamical Systems - A, 2008, 20 (1) : 81-113. doi: 10.3934/dcds.2008.20.81
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