Browsing by Author "Zafer, Agacik"
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Article Citation Count: 0Prescribed Asymptotic Behavior of Nonlinear Dynamic Equations Under Impulsive Perturbations(Springer Basel Ag, 2024) Doğru Akgöl, Sibel; Dogru Akgol, Sibel; MathematicsThe 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.Article Citation Count: 1SECOND ORDER OSCILLATION OF MIXED NONLINEAR DYNAMIC EQUATIONS WITH SEVERAL POSITIVE AND NEGATIVE COEFFICIENTS(Amer inst Mathematical Sciences-aims, 2011) Özbekler, Abdullah; Zafer, Agacik; MathematicsNew oscillation criteria are obtained for superlinear and sublinear forced dynamic equations having positive and negative coefficients by means of nonprincipal solutions.Article Citation Count: 1Wong type oscillation criteria for nonlinear impulsive differential equations(Wiley, 2023) Akgöl, Sibel Doğru; Zafer, Agacik; MathematicsWe 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.