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Second order evolution differential functional equations with infinite delay

100%
Człapiński T., Karpowicz A.
Commentationes Mathematicae
|
2018
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tom 58
|
nr 1-2
EN
We consider a second order semilinear functional evolution equation with infinite delay in a Banach space. We prove the existence of mild solutions for this equation using the measure of noncompactness technique and the Schauder fixed point theorem.
2
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Integrable solutions for quadratic Hammerstein and quadratic Urysohn functional integral equations

100%
El-Sayed A. M. A., Hashem H. H. G.
Commentationes Mathematicae
|
2008
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tom 48
|
nr 2
EN
The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equation have been studied in [3], [6], [7] and [9]. Here We are concerning with the existence of \(L _1\) positive monotonic solutions for the quadratic Hammerstein and quadratic Urysohn functional integral equations.
3
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Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

88%
Olszowy L.
Open Mathematics
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2014
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tom 12
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nr 4
623-635
EN
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.
4
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Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

88%
Yantir A., Kubiaczyk I., Sikorska-Nowak A.
Open Mathematics
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2015
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tom 13
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nr 1
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.
5
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Invariant sets and Knaster-Tarski principle

75%
Leśniak K.
Open Mathematics
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2012
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tom 10
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nr 6
2077-2087
EN
Our aim is to point out the applicability of the Knaster-Tarski fixed point principle to the problem of existence of invariant sets in discrete-time (multivalued) semi-dynamical systems, especially iterated function systems.
6
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Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

63%
Banaś J.
Open Mathematics
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2012
|
tom 10
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nr 6
2003-2011
EN
The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.
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