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