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

Pages: 427 - 435, Issue Special, August 2005

 Abstract        Full Text (200.4K)              

J. Húska - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)
Peter Poláčik - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)
M.V. Safonov - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)

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.

Keywords:  Exponential separation, Harnack inequalities, principal Floquet bundle, robustness, perturbations.
Mathematics Subject Classification:  35K20, 35B05, 35P15, 37L55.

Received: September 2004;      Revised: May 2005;      Published: September 2005.