Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations

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2005, 2005(Special): 427-435. doi: 10.3934/proc.2005.2005.427

Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations

J. Húska ^1, , Peter Poláčik ^1, and M.V. Safonov ^1,

1.	School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States, United States

Received September 2004 Revised May 2005 Published September 2005

Abstract
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We consider the Dirichlet problem for nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz cylinders. We discuss the exponential separation between positive and sign changing solutions and its consequences on principal eigenvalues, eigenfunctions in the time-independent case, and principal Lyapunov exponent and principal Floquet bundle in the general case.

Keywords: principal Floquet bundle, perturbations., Exponential separation, robustness, Harnack inequalities.

Mathematics Subject Classification: 35K20, 35B05, 35P15, 37L5.

Citation: J. Húska, Peter Poláčik, M.V. Safonov. Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Conference Publications, 2005, 2005 (Special) : 427-435. doi: 10.3934/proc.2005.2005.427

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