Existence of solutions for abstract neutral integro-differential equations with unbounded delay
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 691-706
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.
In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.
DOI : 10.1007/s10587-011-0040-z
Classification : 34K30, 34K40, 35R10, 45J05
Keywords: neutral equations; classical solution; analytic semigroup; unbounded delay
@article{10_1007_s10587_011_0040_z,
     author = {Hern\'andez, Eduardo M. and O'Regan, Donal},
     title = {Existence of solutions for abstract neutral integro-differential equations with unbounded delay},
     journal = {Czechoslovak Mathematical Journal},
     pages = {691--706},
     year = {2011},
     volume = {61},
     number = {3},
     doi = {10.1007/s10587-011-0040-z},
     mrnumber = {2853084},
     zbl = {1249.34217},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0040-z/}
}
TY  - JOUR
AU  - Hernández, Eduardo M.
AU  - O'Regan, Donal
TI  - Existence of solutions for abstract neutral integro-differential equations with unbounded delay
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 691
EP  - 706
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0040-z/
DO  - 10.1007/s10587-011-0040-z
LA  - en
ID  - 10_1007_s10587_011_0040_z
ER  - 
%0 Journal Article
%A Hernández, Eduardo M.
%A O'Regan, Donal
%T Existence of solutions for abstract neutral integro-differential equations with unbounded delay
%J Czechoslovak Mathematical Journal
%D 2011
%P 691-706
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0040-z/
%R 10.1007/s10587-011-0040-z
%G en
%F 10_1007_s10587_011_0040_z
Hernández, Eduardo M.; O'Regan, Donal. Existence of solutions for abstract neutral integro-differential equations with unbounded delay. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 691-706. doi: 10.1007/s10587-011-0040-z

[1] Adimy, M., Ezzinbi, K.: A class of linear partial neutral functionaldifferential equations with nondense domain. J. Differ. Equations 147 (1998), 285-332. | DOI | MR

[2] Anguraj, A., Karthikeyan, K.: Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions. Nonlinear Anal., Theory Methods Appl. 70 (2009), 2717-2721. | DOI | MR | Zbl

[3] Balachandran, K., Sakthivel, R.: Existence of solutions of neutral functional integrodifferential equation in Banach spaces. Proc. Indian Acad. Sci., Math. Sci. 109 (1999), 325-332. | DOI | MR

[4] Balachandran, K., Shija, G., Kim, J. H.: Existence of solutions of nonlinear abstract neutral integrodifferential equations. Comput. Math. Appl. 48 (2004), 1403-1414. | DOI | MR | Zbl

[5] Balasubramaniam, P., Park, J. Y., Kumar, A. V. A.: Existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions. Nonlinear Anal., Theory Methods Appl. 71 (2009), 1049-1058. | DOI | MR | Zbl

[6] Benchohra, M., Ntouyas, S. K.: Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces. J. Math. Anal. Appl. 258 (2001), 573-590. | DOI | MR | Zbl

[7] Benchohra, M., Henderson, J., Ntouyas, S. K.: Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces. J. Math. Anal. Appl. 263 (2001), 763-780. | DOI | MR | Zbl

[8] Cannarsa, P., Sforza, D.: Global solutions of abstract semilinear parabolic equations with memory terms. NoDEA, Nonlinear Differ. Equ. Appl. 10 (2003), 399-430. | DOI | MR | Zbl

[9] Chang, Y. V., Anguraj, A., Karthikeyan, K.: Existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71 (2009), 4377-4386. | DOI | MR | Zbl

[10] Clément, Ph., Nohel, J. A.: Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels. SIAM J. Math. Anal. 12 (1981), 514-535. | DOI | MR

[11] Clément, Ph., Prüss, J.: Global existence for a semilinear parabolic Volterra equation. Math. Z. 209 (1992), 17-26. | DOI | MR

[12] Datko, R.: Linear autonomous neutral differential equations in a Banach space. J. Differ. Equations 25 (1977), 258-274. | DOI | MR | Zbl

[13] Dauer, J. P., Balachandran, K.: Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces. J. Math. Anal. Appl. 251 (2000), 93-105. | DOI | MR | Zbl

[14] Gurtin, M. E., Pipkin, A. C.: A general theory of heat conduction with finite wave speeds. Arch. Rat. Mech. Anal. 31 (1968), 113-126. | DOI | MR | Zbl

[15] Henríquez, H. R., Pierri, M., Táboas, P.: Existence of $S$-asymptotically $\omega$-periodic solutions for abstract neutral equations. Bull. Aust. Math. Soc. 78 (2008), 365-382. | DOI | MR

[16] Hernández, E., O'Regan, D.: Existence results for abstract partial neutral differential equations. Proc. Am. Math. Soc. 137 (2009), 3309-3318. | DOI | MR

[17] Hernández, E., O'Regan, D.: $C^{\alpha}$-Hölder classical solutions for non-autonomous neutral differential equations. Discrete Contin. Dyn. Syst. 29 (2011), 241-260. | DOI | MR

[18] Hernández, E., O'Regan, D.: Existence of solutions for abstract non-autonomous neutral differential equations. Can. Math. Bull Accepted.

[19] Hernández, E., Balachandran, K.: Existence results for abstract degenerate neutral functional differential equations. Bull. Aust. Math. Soc. 81 (2010), 329-342. | DOI | MR

[20] Hernández, E., Henríquez, H. R.: Existence results for partial neutral functional integro-differential equation with unbounded delay. J. Math. Anal. Appl. 221 (1998), 452-475. | DOI | MR

[21] Hernández, E.: Existence results for partial neutral integro-differential equations with unbounded delay. J. Math. Anal. Appl. 292 (2004), 194-210. | DOI | MR

[22] Hernández, E., Henríquez, H. R.: Existence of periodic solutions of partial neutral functional differential equation with unbounded delay. J. Math. Anal. Appl. 221 (1998), 499-522. | DOI | MR

[23] Hino, Y., Murakami, S., Naito, T.: Functional-Differential Equations With Infinite Delay. Lecture Notes in Mathematics, 1473. Springer Berlin (1991). | MR

[24] Lunardi, A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems. Progress in Nonlinear Differential Equations and their Applications, 16. Birkhäuser Basel (1995). | MR

[25] Lunardi, A.: On the linear heat equation with fading memory. SIAM J. Math. Anal. 21 (1990), 1213-1224. | DOI | MR | Zbl

[26] Luo, J., Taniguchi, T.: The existence and uniqueness for non-Lipschitz stochastic neutral delay evolution equations driven by Poisson jumps. Stoch. Dyn. 9 (2009), 135-152. | DOI | MR | Zbl

[27] Ntouyas, S. K., O'Regan, D.: Existence results for semilinear neutral functional differential inclusions via analytic semigroups. Acta Appl. Math. 98 (2007), 223-253. | DOI | MR | Zbl

[28] Nunziato, J. W.: On heat conduction in materials with memory. Q. Appl. Math. 29 (1971), 187-204. | DOI | MR | Zbl

[29] Ren, Y., Chen, L.: A note on the neutral stochastic functional differential equation with infinite delay and Poisson jumps in an abstract space. J. Math. Phys. 50 (2009), 082704-082704-8. | DOI | MR

Cité par Sources :