# Article

MSC: 34K30, 34K40, 35R10
Full entry | Fulltext not available (moving wall 24 months)
Keywords:
neutral equations; classical solution; analytic semigroup; unbounded delay
Summary:

References:
[1] Adimy, M., Ezzinbi, K.: A class of linear partial neutral functionaldifferential equations with nondense domain. J. Differ. Equations 147 (1998), 285-332. MR 1633941
[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. MR 2499739 | Zbl 1165.34416
[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. MR 1709339
[4] Balachandran, K., Shija, G., Kim, J. H.: Existence of solutions of nonlinear abstract neutral integrodifferential equations. Comput. Math. Appl. 48 (2004), 1403-1414. MR 2107098 | Zbl 1083.45005
[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. MR 2527524 | Zbl 1171.34054
[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. MR 1835560 | Zbl 0982.45008
[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. MR 1866239 | Zbl 0998.34064
[8] Cannarsa, P., Sforza, D.: Global solutions of abstract semilinear parabolic equations with memory terms. NoDEA, Nonlinear Differ. Equ. Appl. 10 (2003), 399-430. MR 2016932 | Zbl 1052.35085
[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. MR 2548667 | Zbl 1178.34071
[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. MR 0617711
[11] Clément, Ph., Prüss, J.: Global existence for a semilinear parabolic Volterra equation. Math. Z. 209 (1992), 17-26. MR 1143209
[12] Datko, R.: Linear autonomous neutral differential equations in a Banach space. J. Differ. Equations 25 (1977), 258-274. MR 0447743 | Zbl 0402.34066
[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. MR 1790400 | Zbl 0966.45008
[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. MR 1553521 | Zbl 0164.12901
[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. MR 2472273 | Zbl 1183.34122
[16] Hernández, E., O'Regan, D.: Existence results for abstract partial neutral differential equations. Proc. Am. Math. Soc. 137 (2009), 3309-3318. MR 2515400
[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. MR 2725289
[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. MR 2609114 | Zbl 1193.34165
[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. MR 1621730
[21] Hernández, E.: Existence results for partial neutral integro-differential equations with unbounded delay. J. Math. Anal. Appl. 292 (2004), 194-210. MR 2050224
[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. MR 1621738
[23] Hino, Y., Murakami, S., Naito, T.: Functional-Differential Equations With Infinite Delay. Lecture Notes in Mathematics, 1473. Springer Berlin (1991). MR 1122588
[24] Lunardi, A.: Analytic Semigroups and Optimal Regularity in Parabolic Problems. Progress in Nonlinear Differential Equations and their Applications, 16. Birkhäuser Basel (1995). MR 1329547
[25] Lunardi, A.: On the linear heat equation with fading memory. SIAM J. Math. Anal. 21 (1990), 1213-1224. MR 1062400 | Zbl 0716.35031
[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. MR 2502478 | Zbl 1167.60336
[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. MR 2338388 | Zbl 1134.34054
[28] Nunziato, J. W.: On heat conduction in materials with memory. Q. Appl. Math. 29 (1971), 187-204. MR 0295683 | Zbl 0227.73011
[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. MR 2554419 | Zbl 1223.34110

Partner of