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.
Dipartimento di Matematica, Via L. Vanvitelli 1, 06100 Perugia, Italy
Bibliografia
[1] R. Bellman and K. Cooke, Differential Difference Equations, Academic Press, New York, 1963.
[2] P. Brandi and R. Ceppitelli, Existence, uniqueness and continuous dependence for hereditary differential equations, J. Differential Equations 81 (1989), 317-339.
[3] P. Brandi and R. Ceppitelli, A new graph topology. Connections with the compact-open topology, Appl. Anal., to appear.
[4] R. Ceppitelli and L. Faina, Differential equations with hereditary structure induced by a Volterra type property, submitted for publication.
[5] P. C. Das and N. Parhi, On a functional-differential equation of neutral type, J. Math. Anal. Appl. 35 (1971), 67-82.
[6] R. Driver, Existence and continuous dependence of solutions of a neutral functional-differential equation, Arch. Rational Mech. Ann. 19 (1965), 149-166.
[7] L. Faina, Equivalent hereditary structures for a class of functional differential equations, submitted for publication.
[8] J. K. Hale, Theory of Functional Differential Equations, Appl. Math. Sci. 3, Springer, 1977.
[9] J. K. Hale and M. A. Cruz, Existence, uniqueness, and continuous dependence for hereditary systems, Ann. Mat. Pura Appl. 85 (1970), 63-82.
[10] J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkc. Ekvac. 21 (1978), 11-41.
[11] J. K. Hale and K. R. Meyer, A class of functional equations of neutral type, Mem. Amer. Math. Soc. 76 (1967).
[12] D. Henry, Linear autonomous neutral functional differential equations, J. Differential Equations 15 (1974), 106-128.
[13] M. Kisielewicz, Some generic properties of functional-differential equations of neutral type, J. Math. Anal. Appl. 97 (1984), 229-244.
[14] W. R. Melvin, Topologies for nonlinear functional differential equations, J. Differential Equations 13 (1973), 24-31.
[15] W. R. Melvin, A class of neutral functional-differential equations, J. Differential Equations 12 (1972), 524-534.
[16] Z. Wang and J. Wu, Neutral functional differential equations with infinite delay, Funkc. Ekvac. 28 (1985), 157-170.