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Bounded solutions of nonlinear Cauchy problems

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  • Josef Kreulich

Abstract

For a given closed and translation invariant subspace Y of the bounded and uniformly continuous functions, we will give criteria for the existence of solutions u ∈ Y to the equation u ′ ( t ) + A ( u ( t ) ) + ω u ( t ) ∠f ( t ) , t ∈ ℠, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u ′ ( t ) + A ( u ( t ) ) + ω u ( t ) ∠f ( t ) , t > 0 , u ( 0 ) = u 0 , in general Banach spaces, where A denotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the space Y are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior.

Suggested Citation

  • Josef Kreulich, 2002. "Bounded solutions of nonlinear Cauchy problems," Abstract and Applied Analysis, Hindawi, vol. 7, pages 1-25, January.
    • Handle: RePEc:hin:jnlaaa:373218
    DOI: 10.1155/S1085337502208015
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