Integral manifolds of nonautonomous evolution differential equations (Q1274057)

In this paper, the existence of an integral manifold for the nonlinear nonautonomous equation \[ d_tu+ Au+ f(u,t)= 0\tag{1} \] in an abstract Hilbert space \(H\) is considered. Under some natural spectral condition on the positive selfadjoint operator \(A\) and the nonlinear term \(f(u,t)\), the existence of an integral manifold for (1) is proved.