Second order semilinear Volterra integrodifferential equation in Banach space

Jan Bochenek

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 3, page 231-241
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jan Bochenek. "Second order semilinear Volterra integrodifferential equation in Banach space." Annales Polonici Mathematici 57.3 (1992): 231-241. <http://eudml.org/doc/275893>.

@article{JanBochenek1992,
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.},
author = {Jan Bochenek},
journal = {Annales Polonici Mathematici},
keywords = {cosine family; semilinear Volterra equation; second order semilinear Volterra integrodifferential equation; Banach space; partial integrodifferential problem},
language = {eng},
number = {3},
pages = {231-241},
title = {Second order semilinear Volterra integrodifferential equation in Banach space},
url = {http://eudml.org/doc/275893},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Jan Bochenek
TI - Second order semilinear Volterra integrodifferential equation in Banach space
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 3
SP - 231
EP - 241
AB - 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.
LA - eng
KW - cosine family; semilinear Volterra equation; second order semilinear Volterra integrodifferential equation; Banach space; partial integrodifferential problem
UR - http://eudml.org/doc/275893
ER -

References

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  1. [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. Zbl0724.34069
  2. [2] H. O. Fattorini, Ordinary differential equation in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105. Zbl0175.15101
  3. [3] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. Zbl0148.12601
  4. [4] C. Travis and G. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412-424. Zbl0406.45014
  5. [5] C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96. Zbl0388.34039

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