| Title:
|
A note on the solutions of a second-order evolution inclusion in non separable Banach spaces (English) |
| Author:
|
Cernea, Aurelian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
307-314 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a Cauchy problem associated to a second-order evolution inclusion in non separable Banach spaces under Filippov type assumptions and we prove the existence of mild solutions. (English) |
| Keyword:
|
Lusin measurable multifunctions |
| Keyword:
|
differential inclusion |
| Keyword:
|
selection |
| MSC:
|
34A60 |
| idZBL:
|
Zbl 06837067 |
| idMR:
|
MR3708775 |
| DOI:
|
10.14712/1213-7243.2015.215 |
| . |
| Date available:
|
2017-11-22T09:20:23Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146903 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Benchohra M., Medjadj I.: Global existence results for second order neutral functional differential equations with state-dependent delay.Comment. Math. Univ. Carolin. 57 (2016), 169–183. MR 3513443 |
| Reference:
|
[4] Bressan A., Colombo G.: Extensions and selections of maps with decomposable values.Studia Math. 90 (1988), 69–86. Zbl 0677.54013, MR 0947921, 10.4064/sm-90-1-69-86 |
| Reference:
|
[5] De Blasi F.S., Pianigiani G.: Evolution inclusions in non separable Banach spaces.Comment. Math. Univ. Carolin. 40 (1999), 227–250. Zbl 0987.34063, MR 1732644 |
| Reference:
|
[6] Filippov A.F.: Classical solutions of differential equations with multivalued right-hand side.SIAM J. Control Optim. 5 (1967), 609–621. MR 0220995, 10.1137/0305040 |
| Reference:
|
[7] Henriquez H.R.: Existence of solutions of nonautonomous second order functional differential equations with infinite delay.Nonlinear Anal. 74 (2011), 3333–3352. MR 2793566, 10.1016/j.na.2011.02.010 |
| Reference:
|
[8] Henriquez H.R., Poblete V., Pozo J.C.: Mild solutions of non-autonomous second order problems with nonlocal initial conditions.J. Math. Anal. Appl. 412 (2014), 1064–1083. Zbl 1317.34144, MR 3147269, 10.1016/j.jmaa.2013.10.086 |
| Reference:
|
[9] Kozak M.: A fundamental solution of a second-order differential equation in a Banach space.Univ. Iagel. Acta. Math. 32 (1995), 275–289. Zbl 0855.34073, MR 1345144 |
| Reference:
|
[10] Kuratowski K., Ryll-Nardzewski C.: A general theorem on selectors.Bull. Acad. Pol. Sci. Math. Astron. Phys. 13 (1965), 397–403. Zbl 0152.21403, MR 0188994 |
| . |
