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On small solutions of delay equations in infinite dimensions (1998)

Huang, S. Z. ; Neerven, J. M. A. M.

Springer

Integral equations and operator theory 31 (1998), S. 178-185

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ISSN: 1420-8989

Keywords: 34K15 ; 34K25 ; 47D06

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract LetX be a Banach space and 1≤p〈∞. LetL be a bounded linear operator fromL p ([−1,0],X) intoX. Consider the delay differential equationu(t)=Lu t ,u(0)=x,u 0=f on the state spaceL p ([−1,0],X). We prove that a mild solutionu(t)=u(t;x,f) is a small solution if and only if the Laplace transform ofu(t;x,f) extends to an entire function. The same result holds for the state spaceC([−1,0],X).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01214249

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