Bounded solutions of nonlinear Cauchy problems

Josef Kreulich

Abstract and Applied Analysis, 2002, vol. 7, issue 12, 637-661

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)) + ωu(t)∍f(t), t ∈ ℝ, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u′(t) + A(u(t)) + ωu(t)∍f(t), t > 0, u(0) = u0, 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.

Date: 2002
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https://doi.org/10.1155/S1085337502208015

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:7:y:2002:i:12:p:637-661

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