  We consider the problem of shadowing for differential equations with grow-up.
We introduce so-called nonuniform shadowing properties (in which size of the
error depends on the point of the phase space) and prove for them analogs of
shadowing lemma. Besides, we prove a theorem about weighted shadowing for
flows. We compactify the system (using Poincare compactification, for example),
apply the results about nonuniform or weighted shadowing to the compactified
system, and then transfer the results back to the initial system using the
decompactification procedure.
