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Article Citation - WoS: 4Citation - Scopus: 3Boundary Value Problems on Half-Line for Second-Order Nonlinear Impulsive Differential Equations(Wiley, 2018) Akgol, S. D.; Zafer, A.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.Article Citation - WoS: 2Citation - Scopus: 1Oscillation of Impulsive Linear Differential Equations With Discontinuous Solutions(Cambridge University Press, 2023) Doǧru Akgöl,S.Sufficient conditions are obtained for the oscillation of a general form of a linear second-order differential equation with discontinuous solutions. The innovations are that the impulse effects are in mixed form and the results obtained are applicable even if the impulses are small. The novelty of the results is demonstrated by presenting an example of an oscillating equation to which previous oscillation theorems fail to apply. © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.Article Citation - WoS: 1Citation - Scopus: 1Wong Type Oscillation Criteria for Nonlinear Impulsive Differential Equations(Wiley, 2023) Akgol, Sibel D.; Zafer, AgacikWe present Wong-type oscillation criteria for nonlinear impulsive differential equations having discontinuous solutions and involving both negative and positive coefficients. We use a technique that involves the use of a nonprincipal solution of the associated linear homogeneous equation. The existence of principal and nonpricipal solutions was recently obtained by the present authors. As in special cases, we have superlinear and sublinear Emden-Fowler equations under impulse effects. It is shown that the oscillatory behavior may change due to impulses. An example is also given to illustrate the importance of the results.Article Citation - Scopus: 3De La Vallee Poussin Inequality for Impulsive Differential Equations(Walter de Gruyter Gmbh, 2021) Akgol, Sibel Dogru; Ozbekler, AbdullahThe 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
