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Article Citation - WoS: 1Citation - Scopus: 1Prescribed Asymptotic Behavior of Nonlinear Dynamic Equations Under Impulsive Perturbations(Springer Basel Ag, 2024) Zafer, Agacik; Dogru Akgol, SibelThe 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 - WoS: 1Existence of Solutions for Impulsive Boundary Value Problems on Infinite Intervals(Ankara Univ, Fac Sci, 2023) Akgöl, Sibel Doğru; Dogru Akgol, SibelThe paper deals with the existence of solutions for a general class of second-order nonlinear impulsive boundary value problems defined on an infinite interval. The main innovative aspects of the study are that the results are obtained under relatively mild conditions and the use of principal and nonprincipal solutions that were obtained in a very recent study. Additional results about the existence of bounded solutions are also provided, and theoretical results are supported by an illustrative example.
