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2015 | 13 | 1 |
Tytuł artykułu

Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose, we introduce an equivalent integral operator to the SLBVP by means of Green’s function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of noncompactness, we prove the existence of the fixed points of the equivalent integral operator. Mönch’s fixed point theorem is used to prove the main result. Finally, we also remark that it is straightforward to guarantee the existence of Carathéodory solutions for the SLBVP if Kuratowski measure of noncompactness is replaced by any axiomatic measure of noncompactness.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
wydano
2015-01-01
otrzymano
2013-06-17
zaakceptowano
2014-06-12
online
2014-10-09
Twórcy
autor
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan, Poland, kuba@amu.edu.pl
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan, Poland, anetas@amu.edu.pl
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0002
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