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This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....
A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.
We study asymptotic properties of solutions for a system of second differential equations with -Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with -Laplacian . Furthermore, we obtain results for a scalar equation.
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