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

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

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