Periodic solutions of non-densely defined delay evolution equations

Khalil Ezzinbi and James H. Liu

International Journal of Stochastic Analysis, 2002, vol. 15, 1-10

Abstract:

We study the finite delay evolution equation { x ' ( t ) = A x ( t ) + F ( t , x t ) , t ≥ 0 , x 0 = ϕ ∈ C ( [ − r , 0 ] , E ) , where the linear operator A is non-densely defined and satisfies the Hille-Yosida condition. First, we obtain some properties of integral solutions for this case and prove the compactness of an operator determined by integral solutions. This allows us to apply Horn's fixed point theorem to prove the existence of periodic integral solutions when integral solutions are bounded and ultimately bounded. This extends the study of periodic solutions for densely defined operators to the non-densely defined operators. An example is given.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:681080

DOI: 10.1155/S1048953302000114

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