Turkish Journal of Mathematics
Monotone positive solutions of impulsive differential equations asymptotic to nonprincipal solutions
Abstract
This study investigates the asymptotic behavior of monotone positive solutions for a general class of nonlinear second-order impulsive differential equations. By employing the principal and nonprincipal solutions of the associated homogeneous equation, we establish the existence of a monotone positive solution asymptotic to a nonprincipal solution at infinity. To achieve this, we also prove a compactness criterion for an effective use of Schauder’s fixed-point theorem. Under suitable conditions, similarly to the classical case, it is demonstrated that a monotone positive solution asymptotic to a nonprincipal solution exists. A concrete example is given to illustrate the results.
DOI
10.55730/1300-0098.3628
Keywords
Second order, impulse, principal and nonprincipal solution, monotone, positive, asymptotic integration
First Page
838
Last Page
849
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
DOĞRU AKGÖL, S, & ZAFER, A (2025). Monotone positive solutions of impulsive differential equations asymptotic to nonprincipal solutions. Turkish Journal of Mathematics 49 (6): 838-849. https://doi.org/10.55730/1300-0098.3628
