Browsing by Author "Akgol, S. Dogru"

Now showing 1 - 3 of 3

Citation - WoS: 4
Citation - Scopus: 4
Asymptotic Representation of Solutions for Second-Order Impulsive Differential Equations
(Elsevier Science inc, 2018) Akgol, S. Dogru; Zafer, A.
We obtain sufficient conditions which guarantee the existence of a solution of a class of second order nonlinear impulsive differential equations with fixed moments of impulses possessing a prescribed asymptotic behavior at infinity in terms of principal and nonprincipal solutions. An example is given to illustrate the relevance of the results. (C) 2018 Elsevier Inc. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 8
Prescribed asymptotic behavior of second-order impulsive differential equations via principal and nonprincipal solutions
(Academic Press inc Elsevier Science, 2021) Akgol, S. Dogru; Zafer, A.
Finding solutions with prescribed asymptotic behavior is a classical problem for differential equations, which is also known as the asymptotic integration problem for differential equations. Very recent results have revealed that the problem is closely related to principal and nonprincipal solutions of a related homogeneous linear differential equation. Such solutions for second-order linear differential equations without impulse effects, first appeared in [W. Leighton, M. Morse, Trans. Amer. Math. Soc. 40 (1936), 252-286]. In the present work we first establish the concept of principal and nonprincipal solutions for second-order linear impulsive differential equations, and then use them to prove the existence of solutions for a class of second-order nonlinear impulsive differential equations, with prescribed asymptotic behavior at infinity in terms of a linear combination of these principal and nonprincipal solutions. Examples and numerical simulations are provided to illustrate the obtained results. (c) 2021 Elsevier Inc. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 1
Principal and Nonprincipal Solutions of Impulsive Dynamic Equations: Leighton and Wong Type Oscillation Theorems
(Springer, 2023) Zafer, A.; Akgol, S. Dogru
Principal and nonprincipal solutions of differential equations play a critical role in studying the qualitative behavior of solutions in numerous related differential equations. The existence of such solutions and their applications are already documented in the literature for differential equations, difference equations, dynamic equations, and impulsive differential equations. In this paper, we make a contribution to this field by examining impulsive dynamic equations and proving the existence of such solutions for second-order impulsive dynamic equations. As an illustration, we prove the famous Leighton and Wong oscillation theorems for impulsive dynamic equations. Furthermore, we provide supporting examples to demonstrate the relevance and effectiveness of the results.