Browsing by Author "Akgol, Sibel Dogru"

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Citation - WoS: 1
Citation - Scopus: 2
Asymptotic Equivalence of Impulsive Dynamic Equations on Time Scales
(Hacettepe Univ, Fac Sci, 2023) Akgol, Sibel Dogru; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions. To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions. Not only the time scale extensions of former results have been obtained, but also improved for impulsive differential equations defined on the real line. Some illustrative examples are also provided, including an application to a generalized Duffing equation.
Citation - WoS: 1
Citation - Scopus: 2
Existence of Solutions for First Order Impulsive Periodic Boundary Value Problems on Time Scales
(Univ Nis, Fac Sci Math, 2023) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, M. Eymen; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper we study a class of first order impulsive periodic boundary value problems on time scales. We give conditions under which the considered problem has at least one and at least two solutions. The arguments are based upon recent fixed point index theory in cones of Banach spaces for a k-set contraction perturbed by an expansive operator. An example is given to illustrate the obtained result.
Citation - WoS: 1
Citation - Scopus: 2
Existence of Solutions for Odd-Order Multi-Point Impulsive Boundary Value Problems on Time Scales
(Walter de Gruyter Gmbh, 2022) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, Murat Eymen; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Using a fixed point theorem due to Schaefer, the existence of solutions for an odd-order m-point impulsive boundary value problem on time scales is obtained. The problem considered is of general form, where both the differential equation and the impulse effects are nonlinear. Illustrative examples are provided.
Citation - Scopus: 3
De La Vallee Poussin Inequality for Impulsive Differential Equations
(Walter de Gruyter Gmbh, 2021) Akgol, Sibel Dogru; Ozbekler, Abdullah; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The de la Vallee Poussin inequality is a handy tool for the investigation of disconjugacy, and hence, for the oscillation/nonoscillation of differential equations. The results in this paper are extensions of former those of Hartman and Wintner [Quart. Appl. Math. 13 (1955), 330-332] to the impulsive differential equations. Although the inequality first appeared in such an early date for ordinary differential equations, its improved version for differential equations under impulse effect never has been occurred in the literature. In the present study, first, we state and prove a de la Vallee Poussin inequality for impulsive differential equations, then we give some corollaries on disconjugacy. We also mention some open problems and finally, present some examples that support our findings. (C) 2021 Mathematical Institute Slovak Academy of Sciences