Bounded solutions of nonlinear Cauchy problems. (24th December 2002) - Kreulich, Josef
Abstract : For a given closed and translation invariant subspaceY of the bounded and uniformly continuous functions, we will give criteria for the existence of solutionsu ∈ Y to the equationu ′ ( t ) + A ( u ( t ) ) + ω u ( t ) ∍ f ( t ), t ∈ ℝ, or of solutionsu asymptotically close toY for the inhomogeneous differential equationu ′ ( t ) + A ( u ( t ) ) + ω u ( t ) ∍ f ( t ), t > 0, u ( 0 ) = u 0, in general Banach spaces, whereA denotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the spaceY are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior.