Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.
- Differential equations in a Banach space
- Stability of solutions
- stability of solutions
- differential equations in a Banach space