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Abstrakty
The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.
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Daty
otrzymano
2015-06-15
zaakceptowano
2015-09-24
online
2015-10-16
Twórcy
autor
- Laboratoire SAMM, Université Paris 1 Panthéon-Sorbonne, centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France,
autor
- Laboratoire SAMM, Université Paris 1 Panthéon-Sorbonne, centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France,
Bibliografia
- [1] M. Adimy, Integrated semigroups and delay differential equations, J. Math. Anal. Appl. 177 (1993), 125-134.
- [2] J.-P. Aubin, Abstract and applied analysis, Wiley-Interscience, New York, 1977.
- [3] H.T. Banks, Representation of solutions of linear functional differential equations, Differential Equations 5 (1969), 399-409.
- [4] J. Blot, On the almost everywhere continuity, arXiv: 1411.3582v1[math.OC] 13 Nov 2014.
- [5] L. Chambadal, and J.-L. Ovaert, Cours de mathématiques; tome 2 : analyse II, Gauthier-Villars, Paris, 1972.
- [6] J. Dieudonné, Éléments d’analyse; tome 1: fondements de l’analyse moderne, French edition, Gauthier-Villars, Paris, 1969.
- [7] W. Fleming, Functions of several variables, Springer-Verlag, New York, 1977.
- [8] J. Genet, Mesure et intégration, Librairie Vuibert, Paris, 1976.
- [9] J.K. Hale, and M.S. Verduyn Lunel, Introduction to functional differential equations, Springer-Verlag, New York, 1991.
- [10] H. Helson, Harmonic analysis, Wadsworth, Inc., Belmont, California, 1991.
- [11] L.V. Kantorovitch, and G.P. Akilov, Analyse fonctionnelle, tome 1: opérateurs et fonctionnelles linéaires, French edition, MIR, Moscow, 1981.
- [12] A.N. Kolmogorov, and S.V. Fomin, Éléments de la théorie des fonctions et de l’analyse fonctionnelle, French edition, MIR, Moscow, 1974.
- [13] S. Lang, Real and functional analysis, Third edition, Springer-Verlag, New York, 1983.
- [14] L.A. Liusternik, and V.J. Sobolev, Elements of functional analysis, English edition, Frederick Ungar Publishing Co., New York, 1961.
- [15] L. Maniar, Équations différentielles à retard par la méthode d’extrapolation, Port. Math. 54 (1997), 101-113.
- [16] S.-I. Nakagiri, Structural properties of functional differential equations in Banach spaces, Osaka J.Math. 25 (1988), 353-398.
- [17] E. Ramis, C. Deschamps, and J. Odoux, Cours de mathématiques spéciales; tome 3: topologie et éléments d’analyse, Third edition, Masson, Paris, 1991.
- [18] E. Ramis, C. Deschamps, and J. Odoux, Cours de mathématiques spéciales; tome 4: séries et équations différentielles, Third edition, Masson, Paris, 1977.
- [19] F. Riesz and B. Sz. Nagy, Leçons d’analyse fonctionnelle, Sixth edition, Gauthier-Villars, Paris, 1975.
- [20] W. Rudin, Real and complex analysis, McGraw-Hill Book Comp., Singapore, 1987.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_msds-2015-0006