Browsing by Author "Doğru Akgöl, Sibel"

Now showing 1 - 3 of 3

Citation Count: 3
Boundary value problems on half-line for second-order nonlinear impulsive differential equations
(Wiley, 2018) Akgol, S. D.; Zafer, A.; Mathematics
We obtain sufficient conditions for existence and uniqueness of solutions of boundary value problems on half-line for a class of second-order nonlinear impulsive differential equations. Our technique is different than the traditional ones, as it is based on asymptotic integration method involving principal and nonprincipal solutions. Examples are provided to illustrate the relevance of the results.
Citation Count: 6
Leighton and Wong type oscillation theorems for impulsive differential equations
(Pergamon-elsevier Science Ltd, 2021) Akgol, S. D.; Zafer, A.; Mathematics
We obtain the well-known Leighton and Wong oscillation theorems for a general class of second-order linear impulsive differential equations by making use of the recently established results on the existence of nonprincipal solutions. The results indicate that the oscillation character of solutions may be altered by the impulsive perturbations, which is not the case in most published works. Another difference is that the equations are quite general in the sense that the impulses are allowed to appear on both solutions and their derivatives. Examples are also given to illustrate the importance of the results. (C) 2021 Elsevier Ltd. All rights reserved.
Citation Count: 0
Prescribed Asymptotic Behavior of Nonlinear Dynamic Equations Under Impulsive Perturbations
(Springer Basel Ag, 2024) Zafer, Agacik; Dogru Akgol, Sibel; Mathematics
The asymptotic integration problem has a rich historical background and has been extensively studied in the context of ordinary differential equations, delay differential equations, dynamic equations, and impulsive differential equations. However, the problem has not been explored for impulsive dynamic equations due to the lack of essential tools such as principal and nonprincipal solutions, as well as certain compactness results. In this work, by making use of the principal and nonprincipal solutions of the associated linear dynamic equation, recently obtained in [Acta Appl. Math. 188, 2 (2023)], we investigate the asymptotic integration problem for a specific class of nonlinear impulsive dynamic equations. Under certain conditions, we prove that the given impulsive dynamic equation possesses solutions with a prescribed asymptotic behavior at infinity. These solutions can be expressed in terms of principal and nonprincipal solutions as in differential equations. In addition, the necessary compactness results are also established. Our findings are particularly valuable for better understanding the long-time behavior of solutions, modeling real-world problems, and analyzing the solutions of boundary value problems on semi-infinite intervals.