Applications to Kolmogorov Systems of Parabolic Equations

Spectral theory for linear parabolic problems is a basic tool for the study of nonlinear parabolic problems. In this chapter, we discuss some applications of the principal spectral theory developed in previous chapters to uniform persistence of systems of random and nonautonomous nonlinear equations of Kolmogorov type. We first consider applications to random and nonautonomous nonlinear equations of Kolmogorov type, and then consider applications to systems of such equations.