Journal
SBORNIK MATHEMATICS
Volume 208, Issue 8, Pages 1246-1259Publisher
TURPION LTD
DOI: 10.1070/SM8895
Keywords
differential equations in a Banach space; stability of solutions
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Stability problems for solutions of the differential equation u'(t) = Au + epsilon B(t,u) in a Banach space are considered. It is assumed that for epsilon = 0 this equation generates a uniformly bounded group of class C-0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small epsilon. A linearization principle is proved for this equation under certain conditions on the operator B.
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