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ArticleOriginal scientific text

Title

Second order semilinear Volterra integrodifferential equation in Banach space

Authors 1

Affiliations

  1. Institute of Mathematics, Technical University of Cracow, Warszawska 24, 31-155 Kraków Poland

Abstract

By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.

Keywords

ENG
cosine family, semilinear Volterra equation

Bibliography

  1. J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166.
  2. H. O. Fattorini, Ordinary differential equation in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105.
  3. T. Kato, Perturbation Theory for Linear Operators, Springer, 1966.
  4. C. Travis and G. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412-424.
  5. C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96.
Annales Polonici Mathematici
1992/57/3
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Pages:
231-241
Main language of publication
English
Received
1991-06-05
Accepted
1992-02-15
Published
1992
Exact and natural sciences