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

J. Húska; Peter Poláčik; M.V. Safonov

doi:10.3934/proc.2005.2005.427

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2005, Volume 2005: 427-435. Doi: 10.3934/proc.2005.2005.427 open access

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

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

Received: August 31, 2004

Revised: April 30, 2005

Published: August 2005

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Abstract

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.

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Mathematics Subject Classification: 35K20, 35B05, 35P15, 37L55.

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