| Title:
|
Existence and controllability for nondensely defined partial neutral functional differential inclusions (English) |
| Author:
|
Ezzinbi, Khalil |
| Author:
|
Lalaoui Rhali, Soumia |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
321-340 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give sufficient conditions for the existence of integral solutions for a class of neutral functional differential inclusions. The assumptions on the generator are reduced by considering nondensely defined Hille-Yosida operators. Existence and controllability results are established by combining the theory of addmissible multivalued contractions and Frigon's fixed point theorem. These results are applied to a neutral partial differential inclusion with diffusion. (English) |
| Keyword:
|
nondensely operator |
| Keyword:
|
neutral differential inclusion |
| Keyword:
|
multivalued map |
| Keyword:
|
fixed point |
| Keyword:
|
controllability |
| Keyword:
|
C$_{0}$-semigroup |
| MSC:
|
34A60 |
| MSC:
|
34K35 |
| MSC:
|
93B05 |
| idZBL:
|
Zbl 06486914 |
| idMR:
|
MR3419965 |
| DOI:
|
10.1007/s10492-015-0098-2 |
| . |
| Date available:
|
2015-05-15T07:42:42Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144266 |
| . |
| Reference:
|
[1] Abada, N., Benchohra, M., Hammouche, H.: Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions.J. Differ. Equations 246 (2009), 3834-3863. Zbl 1171.34052, MR 2514728, 10.1016/j.jde.2009.03.004 |
| Reference:
|
[2] Abada, N., Benchohra, M., Hammouche, H., Ouahab, A.: Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces.Discuss. Math., Differ. Incl. Control Optim. 27 (2007), 329-347. Zbl 1145.34047, MR 2413817, 10.7151/dmdico.1088 |
| Reference:
|
[3] Adimy, M., Ezzinbi, K.: A class of linear partial neutral functional differential equations with nondense domain.J. Differ. Equations 147 (1998), 285-332. Zbl 0915.35109, MR 1633941, 10.1006/jdeq.1998.3446 |
| Reference:
|
[4] Adimy, M., Ezzinbi, K.: Existence and linearized stability for partial neutral functional differential equations with nondense domains.Differ. Equ. Dyn. Syst. 7 (1999), 371-417. Zbl 0983.34075, MR 1862582 |
| Reference:
|
[5] Belmekki, M., Benchohra, M., Ezzinbi, K., Ntouyas, S.: Existence results for semilinear perturbed functional differential equations of neutral type with infinite delay.Mediterr. J. Math. 7 (2010), 1-18. Zbl 1214.34065, MR 2645898, 10.1007/s00009-010-0023-6 |
| Reference:
|
[6] Belmekki, M., Benchohra, M., Górniewicz, L., Ntouyas, S. K.: Existence results for perturbed semilinear functional differential inclusions with infinite delay.Nonlinear Anal. Forum 13 (2008), 135-156. MR 2808070 |
| Reference:
|
[7] Belmekki, M., Benchohra, M., Ntouyas, S. K.: Existence results for semilinear perturbed functional differential equations with nondensely defined operators.Fixed Point Theory Appl. 2006 (2006), 13 pages, Article ID 43696. Zbl 1150.34592, MR 2270321 |
| Reference:
|
[8] Benchohra, M., Górniewicz, L., Ntouyas, S. K., Ouahab, A.: Controllability results for nondensely defined semilinear functional differential equations.Z. Anal. Anwend. 25 (2006), 311-325. Zbl 1101.93007, MR 2251956, 10.4171/ZAA/1291 |
| Reference:
|
[9] Benchohra, M., Ouahab, A.: Controllability results for functional semilinear differential inclusions in Fréchet spaces.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 61 (2005), 405-423. Zbl 1086.34062, MR 2123084, 10.1016/j.na.2004.12.002 |
| Reference:
|
[10] Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Mathematics 580 Springer, Berlin (1977). Zbl 0346.46038, MR 0467310, 10.1007/BFb0087688 |
| Reference:
|
[11] Prato, G. Da, Sinestrari, E.: Differential operators with non dense domain.Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 14 (1987), 285-344. Zbl 0652.34069, MR 0939631 |
| Reference:
|
[12] Frigon, M.: Fixed point results for multivalued contractions on gauge spaces.Set Valued Mappings with Applications in Nonlinear Analysis R. Agarwal et al. Ser. Math. Anal. Appl. 4 Taylor & Francis, London (2002), 175-181. Zbl 1013.47013, MR 1938847 |
| Reference:
|
[13] Hale, J. K.: Partial neutral functional differential equations.Rev. Roum. Math. Pures Appl. 39 (1994), 339-344. Zbl 0817.35119, MR 1317773 |
| Reference:
|
[14] Henderson, J., Ouahab, A.: Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces.Electron. J. Qual. Theory Differ. Equ. 2005 (2005), 17 pages. Zbl 1111.34045, MR 2176192 |
| Reference:
|
[15] Hernandez, M. E.: A comment on the papers: Controllability results for functional semilinear differential inclusions in Fréchet spaces and Controllability of impulsive neutral functional differential inclusions with infinite delay.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66 (2007), 2243-2245. Zbl 1290.34077, MR 2311027 |
| Reference:
|
[16] Mahmudov, E. N.: Approximation and Optimization of Discrete and Differential Inclusions.Elsevier Insights Elsevier, Amsterdam (2011). Zbl 1235.65002, MR 3293164 |
| Reference:
|
[17] Mahmudov, E. N., Mastaliyeva, D.: Optimization of neutral functional-differential inclusions.J. Dyn. Control Syst. 21 (2015), 25-46. Zbl 1317.49033, MR 3297939, 10.1007/s10883-014-9215-x |
| Reference:
|
[18] Mordukhovich, B. S., Wang, L.: Optimal control of neutral functional-differential inclusions.SIAM J. Control Optimization 43 (2004), 111-136. Zbl 1208.49031, MR 2082695, 10.1137/S0363012902420376 |
| Reference:
|
[19] Wu, J.: Theory and Applications of Partial Functional Differential Equations.Applied Mathematical Sciences 119 Springer, New York (1996). Zbl 0870.35116, MR 1415838, 10.1007/978-1-4612-4050-1 |
| Reference:
|
[20] Wu, J., Xia, H.: Self-sustained oscillations in a ring array of coupled lossless transmission lines.J. Differ. Equations 124 (1996), 247-278. Zbl 0840.34080, MR 1368068, 10.1006/jdeq.1996.0009 |
| Reference:
|
[21] Wu, J., Xia, H.: Rotating waves in neutral partial functional differential equations.J. Dyn. Differ. Equations 11 (1999), 209-238. Zbl 0939.35188, MR 1695243, 10.1023/A:1021973228398 |
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