## B. Karasözen, I. V. Konopleva, and
B. V. Loginov

# Differential-algebraic equations in the theory of invariant manifolds for singular equations

## (*Lobachevskii Journal of Mathematics, Vol.20, pp.77-89*)

Analogs of Grobman-Hartman theorem on stable and
unstable manifolds solutions for differential equations in Banach
spaces with degenerate Fredholm operator at the derivative are
proved. Jordan chains tools and the implicit operator theorem are
used. In contrast to the usual evolution equation here the central
manifold appears even for the case of spectrum absence on the
imaginary axis. If on the imaginary axis there is only a finite
number of spectrum points, then the original nonlinear equation is
reduced to two differential--algebraic systems on the center manifold.

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