| Title:
|
On the Solution Set of a Nonconvex Nonclosed Second Order Inclusion (English) |
| Author:
|
Cernea, Aurelian |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
21-28 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions. (English) |
| Keyword:
|
Set-valued contraction, fixed point, solution set |
| MSC:
|
34A60 |
| . |
| Date available:
|
2019-09-27T07:32:59Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703028 |
| . |
| Reference:
|
[1] Baliki, A., Benchohra, M., Graef, J. R.: Global existence and stability of second order functional evolution equations with infinite delay., Electronic J. Qual. Theory Differ. Equations, 2016, no. 23, (2016), pp. 1–10. MR 3498741 |
| Reference:
|
[2] Baliki, A., Benchohra, M., Nieto, J. J.: Qualitative analysis of second-order functional evolution equations., Dynamic Syst. Appl., 24 (2015), pp. 559–572. MR 3444994 |
| 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), pp. 169–183. MR 3513443 |
| Reference:
|
[4] Benchohra, M., Rezzoug, N.: Measure of noncompactness and second-order evolution equations., Gulf J. Math., 4 (2016), pp. 71–79. MR 3518037 |
| Reference:
|
[5] Cernea, A.: On the solution set of some classes of nonconvex nonclosed differential inclusions., Portugaliae Math., 65 (2008), pp. 485–496. MR 2483348, 10.4171/PM/1822 |
| Reference:
|
[6] Cernea, A.: On the solution set of a nonconvex nonclosed Sturm-Liouville type differential inclusion., Comment. Math., 49 (2009), pp. 139–146. MR 2591179 |
| Reference:
|
[7] Cernea, A.: On the solution set of a nonconvex nonclosed hyperbolic differential inclusion of third order., J. Nonlinear Convex Anal., 17 (2016), pp. 1171–1179. MR 3540236 |
| Reference:
|
[8] Henriquez, H. R.: Existence of solutions of nonautonomous second order functional differential equations with infinite delay., Nonlinear Anal., 74 (2011), pp. 3333–3352. MR 2793566, 10.1016/j.na.2011.02.010 |
| Reference:
|
[9] 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), pp. 1064–1083. MR 3147269, 10.1016/j.jmaa.2013.10.086 |
| Reference:
|
[10] Kozak, M.: A fundamental solution of a second-order differential equation in a Banach space., Univ. Iagel. Acta. Math., 32 (1995), pp. 275–289. MR 1345144 |
| Reference:
|
[11] Marano, S.: Fixed points of multivalued contractions with nonclosed, nonconvex values., Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 5 (1994), pp. 203–212. MR 1298263 |
| Reference:
|
[12] Marano, S., Staicu, V.: On the set of solutions to a class of nonconvex nonclosed differential inclusions., Acta Math. Hungar., 76 (1997), pp. 287–301. MR 1459237, 10.1023/A:1006533606338 |
| . |
