Second order semilinear Volterra integrodifferential equation in Banach space
Jan Bochenek
Annales Polonici Mathematici, Tome 57 (1992), p. 231-241 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:275893 
@article{bwmeta1.element.bwnjournal-article-apmv57z3p231bwm,
     author = {Jan Bochenek},
     title = {Second order semilinear Volterra integrodifferential equation in Banach space},
     journal = {Annales Polonici Mathematici},
     volume = {57},
     year = {1992},
     pages = {231-241},
     zbl = {0786.45013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p231bwm}
}

Jan Bochenek. Second order semilinear Volterra integrodifferential equation in Banach space. Annales Polonici Mathematici, Tome 57 (1992) pp. 231-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p231bwm/

[000] [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166. | Zbl 0724.34069

[001] [2] H. O. Fattorini, Ordinary differential equation in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105. | Zbl 0175.15101

[002] [3] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. | Zbl 0148.12601

[003] [4] C. Travis and G. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412-424. | Zbl 0406.45014

[004] [5] C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96. | Zbl 0388.34039