Multivalued second order differential problem
Let $K$ be a closed convex cone with nonempty interior in a real Banach space and let $F,G,Hcolon K o cc(K)$ be three given continuous additive set-valued functions. We study the existence and uniqueness of a solution of the second order differential problem $$ D^2Phi (t,x) = Phi (...
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Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2012-04-01
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Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/115 |
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doaj-2aaa6bbb4389464d97001352b6ed5a462020-11-24T21:01:59ZdeuWydawnictwo Naukowe Uniwersytetu PedagogicznegoAnnales Universitatis Paedagogicae Cracoviensis: Studia Mathematica 2081-545X2012-04-011115367Multivalued second order differential problemEwelina Mainka-NiemczykLet $K$ be a closed convex cone with nonempty interior in a real Banach space and let $F,G,Hcolon K o cc(K)$ be three given continuous additive set-valued functions. We study the existence and uniqueness of a solution of the second order differential problem $$ D^2Phi (t,x) = Phi (t,H(x)) $$ $$ Phi (0,x) = F(x),quad DPhi (t,x)|_{t=0} = G(x) $$ for $tgeq 0$ and $xin K$, where $DPhi (t,x)$ and $D^2Phi (t,x)$ denote the Hukuhara derivative and the second Hukuhara derivative of $Phi (t,x)$ with respect to $t$.http://studmath.up.krakow.pl/index.php/studmath/article/view/115 |
collection |
DOAJ |
language |
deu |
format |
Article |
sources |
DOAJ |
author |
Ewelina Mainka-Niemczyk |
spellingShingle |
Ewelina Mainka-Niemczyk Multivalued second order differential problem Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
author_facet |
Ewelina Mainka-Niemczyk |
author_sort |
Ewelina Mainka-Niemczyk |
title |
Multivalued second order differential problem |
title_short |
Multivalued second order differential problem |
title_full |
Multivalued second order differential problem |
title_fullStr |
Multivalued second order differential problem |
title_full_unstemmed |
Multivalued second order differential problem |
title_sort |
multivalued second order differential problem |
publisher |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego |
series |
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
issn |
2081-545X |
publishDate |
2012-04-01 |
description |
Let $K$ be a closed convex cone with nonempty interior in a real Banach space and let $F,G,Hcolon K o cc(K)$ be three given continuous additive set-valued functions. We study the existence and uniqueness of a solution of the second order differential problem $$ D^2Phi (t,x) = Phi (t,H(x)) $$ $$ Phi (0,x) = F(x),quad DPhi (t,x)|_{t=0} = G(x) $$ for $tgeq 0$ and $xin K$, where $DPhi (t,x)$ and $D^2Phi (t,x)$ denote the Hukuhara derivative and the second Hukuhara derivative of $Phi (t,x)$ with respect to $t$. |
url |
http://studmath.up.krakow.pl/index.php/studmath/article/view/115 |
work_keys_str_mv |
AT ewelinamainkaniemczyk multivaluedsecondorderdifferentialproblem |
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1716777013492056064 |