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A note on explicit solutions of certain impulsive fractional differential equations
구남집 충청수학회 2017 충청수학회지 Vol.30 No.1
This paper deals with linear impulsive differential equations involving the Caputo fractional derivative. We provide exact solutions of nonhomogeneous linear impulsive fractional differential equations with constant coefficients by means of the Mittag-Leffler functions.
ON STABILITY OF EXPANSIVE INDUCED HOMEOMORPHISMS ON HYPERSPACES
구남집,이현희 충청수학회 2022 충청수학회지 Vol.35 No.1
In this paper we investigate the topological stability of induced homeomorphisms on a hyperspace. More precisely, we show that an expansive induced homeomorphism on a hyperspace is topologically stable. We also give examples and a diagram about implications to illustrate our results.
Topological stability in hyperspace dynamical systems
구남집,이현희,Nyamdavaa Tsegmid 대한수학회 2020 대한수학회논문집 Vol.35 No.4
In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.
A NOTE ON WEAK EXPANSIVE HOMEOMORPHISMS ON A COMPACT METRIC SPACE
구남집,Tumur Gansukh 충청수학회 2020 충청수학회지 Vol.33 No.1
In this paper we introduce the notion of the expansivity for homeomorphisms on a compact metric space and study some properties concerning weak expansive homeomorphisms. Also, we give some examples to illustrate our results.
구남집,이현희,Nyamdavaa Tsegmid 대한수학회 2024 대한수학회보 Vol.61 No.1
In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a $G_{\delta}$ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in $X$. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.
A note on generalized singular Gronwall inequalities
강보원,구남집 충청수학회 2018 충청수학회지 Vol.31 No.1
This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.
h-Stability for linear differential systems via t-quasisimilarity
최성규,구남집 충청수학회 2008 충청수학회지 Vol.21 No.1
We study $h$-stability for linear differential systems by using $t_\infty$-quasisimilarity and Gronwall's inequality.
A NOTE ON CHAIN TRANSITIVITY OF LINEAR DYNAMICAL SYSTEMS
이현희,구남집 충청수학회 2023 충청수학회지 Vol.36 No.2
In this paper we study some topological modes of recurrent sets of linear homeomorphisms of a finite-dimensional topological vector space. More precisely, we show that there are no chain transitive linear homeomorphisms of a finite-dimensional Banach space having the shadowing property. Then, we give examples to illustrate our results.
Stability of linear impulsive differential equations via t∞-similarity
최성규,구남집,류춘미 충청수학회 2013 충청수학회지 Vol.26 No.4
In this paper we investigate h-stability for linear impulsive equations using the notion of t∞-similarity and an impulsive integral inequality.
Stability properties in impulsive differential systems of non-integer order
강보원,구남집 대한수학회 2019 대한수학회지 Vol.56 No.1
In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.