On the Solution Set of a Nonconvex Nonclosed Second Order Inclusion

Cernea, Aurelian

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 21-28

Abstract

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We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions.

How to cite

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Cernea, Aurelian. "On the Solution Set of a Nonconvex Nonclosed Second Order Inclusion." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 21-28. <http://eudml.org/doc/294931>.

@inProceedings{Cernea2017,
abstract = {We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions.},
author = {Cernea, Aurelian},
booktitle = {Proceedings of Equadiff 14},
keywords = {Set-valued contraction, fixed point, solution set},
location = {Bratislava},
pages = {21-28},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {On the Solution Set of a Nonconvex Nonclosed Second Order Inclusion},
url = {http://eudml.org/doc/294931},
year = {2017},
}

TY - CLSWK
AU - Cernea, Aurelian
TI - On the Solution Set of a Nonconvex Nonclosed Second Order Inclusion
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 21
EP - 28
AB - We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions.
KW - Set-valued contraction, fixed point, solution set
UR - http://eudml.org/doc/294931
ER -

References

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  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. MR3147269
  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. MR1345144
  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. MR1298263
  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. MR1459237

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