Turkish Journal of Mathematics
Author ORCID Identifier
ÖZKAN ÖZTÜRK: 0000-0001-6657-7409
ELVAN AKIN: 0000-0002-7301-891X
NESLİHAN NESLİYE PELEN: 0000-0003-1853-3959
Abstract
This paper investigates a third-order nonlinear dynamic equation on arbitrary time scales, a nonempty closed subset of the real numbers, unifying continuous and discrete analyses. We study the qualitative behavior of nonoscillatory solutions and their quasi-derivatives, focusing on their limiting behaviors. The existence of such solutions are established using improper integral criteria and Schauder’s and Knaster’s fixed point theorems. In addition, we establish the criteria for the nonexistence of nonoscillatory solutions. Furthermore, we prove the existence of Kneser-type solutions of the corresponding linear dynamic equation on isolated time scales, addressing an open problem in the literature. Several examples of theoretical results are illustrated on various time scales, including real numbers, integers, and the q-calculus time scale with q > 1.
DOI
10.55730/1300-0098.3610
Keywords
Third-order dynamic equation, oscillation, fixed point theorem, time scales, Kneser solutions
First Page
585
Last Page
602
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
ÖZTÜRK, Ö, AKIN, E, & PELEN, N (2025). Nonoscillatory solutions of third-order nonlinear dynamic equations: Existence and nonexistence. Turkish Journal of Mathematics 49 (5): 585-602. https://doi.org/10.55730/1300-0098.3610
