Bounded solutions of nonlinear Cauchy problems. (24th December 2002)

• Record Type: Journal Article
• Authors: Kreulich, Josef
• Is Part Of: Abstract and applied analysis. Volume 7:Number 12(2002)
• Page Start: 637
• Page End: 661
• Publication Date: 2002-12-24
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337502208015
• Languages: English
• ISSNs: 1085-3375

Abstract

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.