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1
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Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

100%
Banaś J.
Open Mathematics
|
2012
|
tom 10
|
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.
2
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A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

61%
Przeradzki B.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2012-2018
EN
The existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.
3
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Invariant sets and Knaster-Tarski principle

61%
Leśniak K.
Open Mathematics
|
2012
|
tom 10
|
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.
4
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Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

52%
Olszowy L.
Open Mathematics
|
2014
|
tom 12
|
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.
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