Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line (Q1018195)

The author studies the existence of the stable manifold for some nonautonomous evolution equations in Banach spaces. The linear part is time dependent and has an exponential dichotomy. The nonlinear part is Lipschitz continuous and the Lipschitz coefficient is also time dependent. The Lipschitz coefficient function must be in admissible functions spaces which contain \(L_p\) spaces. The results are interesting for applications and generalize some well known established results in the field when the Lipschitz coefficient is constant.