Existence and continuous dependence for a class of neutral functional differential equations
Loris Faina
Annales Polonici Mathematici, Tome 63 (1996), p. 215-226 / Harvested from The Polish Digital Mathematics Library
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A general result on existence and continuous dependence of the solution for a quite wide class of N.F.D.E. is given. Further, an abstract equivalence is proved for three different formulations of N.F.D.E.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:270012 
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     year = {1996},
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Loris Faina. Existence and continuous dependence for a class of neutral functional differential equations. Annales Polonici Mathematici, Tome 63 (1996) pp. 215-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z3p215bwm/

[000] [1] R. Bellman and K. Cooke, Differential Difference Equations, Academic Press, New York, 1963. | Zbl 0105.06402

[001] [2] P. Brandi and R. Ceppitelli, Existence, uniqueness and continuous dependence for hereditary differential equations, J. Differential Equations 81 (1989), 317-339. | Zbl 0709.34062

[002] [3] P. Brandi and R. Ceppitelli, A new graph topology. Connections with the compact-open topology, Appl. Anal., to appear. | Zbl 0836.54010

[003] [4] R. Ceppitelli and L. Faina, Differential equations with hereditary structure induced by a Volterra type property, submitted for publication. | Zbl 0988.34049

[004] [5] P. C. Das and N. Parhi, On a functional-differential equation of neutral type, J. Math. Anal. Appl. 35 (1971), 67-82. | Zbl 0216.11903

[005] [6] R. Driver, Existence and continuous dependence of solutions of a neutral functional-differential equation, Arch. Rational Mech. Ann. 19 (1965), 149-166. | Zbl 0148.05703

[006] [7] L. Faina, Equivalent hereditary structures for a class of functional differential equations, submitted for publication.

[007] [8] J. K. Hale, Theory of Functional Differential Equations, Appl. Math. Sci. 3, Springer, 1977. | Zbl 0352.34001

[008] [9] J. K. Hale and M. A. Cruz, Existence, uniqueness, and continuous dependence for hereditary systems, Ann. Mat. Pura Appl. 85 (1970), 63-82. | Zbl 0194.41002

[009] [10] J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkc. Ekvac. 21 (1978), 11-41. | Zbl 0383.34055

[010] [11] J. K. Hale and K. R. Meyer, A class of functional equations of neutral type, Mem. Amer. Math. Soc. 76 (1967). | Zbl 0179.20501

[011] [12] D. Henry, Linear autonomous neutral functional differential equations, J. Differential Equations 15 (1974), 106-128. | Zbl 0294.34047

[012] [13] M. Kisielewicz, Some generic properties of functional-differential equations of neutral type, J. Math. Anal. Appl. 97 (1984), 229-244. | Zbl 0524.34068

[013] [14] W. R. Melvin, Topologies for nonlinear functional differential equations, J. Differential Equations 13 (1973), 24-31. | Zbl 0238.34101

[014] [15] W. R. Melvin, A class of neutral functional-differential equations, J. Differential Equations 12 (1972), 524-534. | Zbl 0234.34083

[015] [16] Z. Wang and J. Wu, Neutral functional differential equations with infinite delay, Funkc. Ekvac. 28 (1985), 157-170. | Zbl 0553.34044