# Second order semilinear Volterra integrodifferential equation in Banach space

Annales Polonici Mathematici (1992)

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

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topJan 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

top- [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. Zbl0724.34069
- [2] H. O. Fattorini, Ordinary differential equation in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105. Zbl0175.15101
- [3] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. Zbl0148.12601
- [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] 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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