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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: 22Citation - Scopus: 21Principal and Nonprincipal Solutions of Impulsive Differential Equations With Applications(Elsevier Science inc, 2010) Ozbekler, A.; Zafer, A.We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results. (C) 2010 Elsevier Inc. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4Asymptotic 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.Article Citation - WoS: 8Citation - Scopus: 7Leighton and Wong Type Oscillation Theorems for Impulsive Differential Equations(Pergamon-elsevier Science Ltd, 2021) Akgol, S. D.; Zafer, A.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.
