Browsing by Author "Sikorska-Nowak, Aneta"

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Citation - WoS: 2
Citation - Scopus: 2
Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces
(De Gruyter Open Ltd peter.golla@degruyter.com, 2015) Ahmet Yantir; Ireneusz Kubiaczyk; Aneta Sikorska-Nowak; Yantir, Ahmet; Kubiaczyk, Ireneusz; Sikorska-Nowak, Aneta
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. © 2016 Elsevier B.V. All rights reserved.
Citation - WoS: 12
EXISTENCE OF SOLUTIONS OF THE DYNAMIC CAUCHY PROBLEM IN BANACH SPACES
(DE GRUYTER POLAND SP Z O O, 2012) Mieczyslaw Cichon; Ireneusz Kubiaczyk; Aneta Sikorska-Nowak; Ahmet Yantir; Yantir, Ahmet; Cichon, Mieczyslaw; Kubiaczyk, Ireneusz; Sikorska-Nowak, Aneta
In this paper we obtain the existence of solutions and Caratheodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales x(triangle)(t) = f(tx(t)) x(0)=x(o) t is an element of I-a where f is continuous or f satisfies Caratheodory conditions and some conditions expressed in terms of measures of noncompactness. The Manch fixed point theorem is used to prove the main result which extends these obtained for real valued functions.
Citation - WoS: 4
Citation - Scopus: 4
Nonlinear Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces
(BELGIAN MATHEMATICAL SOC TRIOMPHE, 2013) Ahmet Yantir; Ireneusz Kubiaczyk; Aneta Sikorska-Nowak; Yantir, Ahmet; Kubiaczyk, Ireneusz; Sikorska-Nowak, Aneta
This paper is devoted to prove the existence of solutions of the nonlinear Sturm-Liouville boundary value problem on time scales in Banach spaces. We obtain the sufficient conditions for the existence of solutions in terms of Kuratowski measure of noncompactness. Winch's fixed point theorem is used to prove the main result. By the unification property of time scales our result is valid for Sturm-Liouville differential equations and difference equations but more interestingly by the extension property it is also valid for Sturm-Liouville q-difference equation.