Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations

摘要: Abstract The purpose of the paper is to extend principal eigenvalue and eigenfunction theory for time independent periodic parabolic equations random general nonautonomous ones. In case, a notion Lyapunov exponent serving as an analog introduced. It shown that deterministic simple multiplicity. also there one-dimensional invariant subbundle corresponding solutions are globally defined same sign, which serves eigenfunction. addition, monotonicity with respect zero-order terms both in equation boundary condition proved. When second- first-order deterministic, it proved greater than or equal associated time-averaged equation. concepts spectrum, eigenvalue, exponents As known, spectrum compact interval. contains all exponents. second independent, lower estimate infimum given