FC - DM | Dissertações de Mestrado e Teses de Doutoramento
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- Generalized Trichotomies: robustness and global and local invariant manifoldsPublication . Costa, Cristina Maria Gomes Tomás da; Bento, António Jorge GomesIn a Banach space, given a differential equation v′(t) = A(t)v(t), with an initial condition v(s) = vs and that admits a generalized trichotomy, we studied which type of conditions we need to impose to the linear perturbations B so that v′(t) = [A(t) + B(t)] v(t) continues to admit a generalized trichotomy, that is, we studied the robustness of generalized trichotomies. In the same way, it was also the aim of our work the study of a differential equation with another type of nonlinear perturbations, v′(t) = A(t)v(t) + f(t, v). We sought conditions to impose on the function f so that the new perturbed equation would admit a global Lipschitz invariant manifold as well as the necessary conditions for the existence of local Lipschitz invariant manifolds.