Second order differential equations in Banach space

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The theory of second-order differential equations in Banach space is surveyed. An introduction of certain selected aspects of the subject is attempted, rather than a complete discussion. References to various proofs are given, but not the proofs themselves. The bulk of the material concerns linear second-order differential equations, a subject linked intimately with the theory of strongly continuous cosine families of bounded linear operators in Banach space. Results are also presented on nonlinear second-order equations having a special semilinear form. The following topics are included: the basic theory of strongly continuous cosine families in Banach space, and the fundamental generation ... continued below

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Pages: 32

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Travis, C.C. & Webb, G.F. Creation Date: Unknown.

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Description

The theory of second-order differential equations in Banach space is surveyed. An introduction of certain selected aspects of the subject is attempted, rather than a complete discussion. References to various proofs are given, but not the proofs themselves. The bulk of the material concerns linear second-order differential equations, a subject linked intimately with the theory of strongly continuous cosine families of bounded linear operators in Banach space. Results are also presented on nonlinear second-order equations having a special semilinear form. The following topics are included: the basic theory of strongly continuous cosine families in Banach space, and the fundamental generation theorem of Sova--Da Prato--Giusti--Fattorini; the problem of converting an abstract second-order linear differential equation to an abstract first-order differential system; perturbations of the infinitesimal generator of a strongly continuous cosine family, and the approximation theorem of Konishi--Goldstein; the special properties of compactness, uniform continuity, and inhomogeneous equations for strongly continuous cosine families; and abstract semilinear second-order initial-value problems in which the linear term is a cosine family generator. (RWR)

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Pages: 32

Notes

Dep. NTIS, PC A03/MF A01.

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  • Conference on differential equations in abstract spaces, Arlington, TX, USA, 8 Jun 1977

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  • Report No.: CONF-770699-1
  • Grant Number: W-7405-ENG-26
  • Office of Scientific & Technical Information Report Number: 5259466
  • Archival Resource Key: ark:/67531/metadc1070110

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  • Feb. 4, 2018, 10:51 a.m.

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  • March 30, 2018, 12:24 p.m.

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Travis, C.C. & Webb, G.F. Second order differential equations in Banach space, article, Date Unknown; Tennessee. (digital.library.unt.edu/ark:/67531/metadc1070110/: accessed June 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.