On the robustness of nonuniform exponential trichotomies (Q905839)

Consider a linear evolution equation \[ x'(t)=A(t)x(t) \] in a Banach space \(X\), where \(A(t)\in\mathcal{B}(X)\) is of class \(C^1\). It is proved that the existence of a nonuniform exponential trichotomies persists for the perturbed equation \[ x'(t)=[A(t)+B(t,\lambda)]x(t) \] for sufficiently small perturbation \(B(t,\lambda)\in\mathcal{B}(X)\) of the class \(C^1\). It is shown that stable, unstable and center subspaces are of the class \(C^1\) in \(\lambda\).