Nonoscillatory Solutions of Third-order Nonlinear Dynamic Equations: Existence and Nonexistence
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.
Recommended Citation
Ö. Öztürk et al., "Nonoscillatory Solutions of Third-order Nonlinear Dynamic Equations: Existence and Nonexistence," Turkish Journal of Mathematics, vol. 49, no. 5, pp. 585 - 602, Scientific and Technological Research Council of Turkiye (Tubitak), Jan 2025.
The definitive version is available at https://doi.org/10.55730/1300-0098.3610
Department(s)
Mathematics and Statistics
Keywords and Phrases
34A34; 34N05; 39A05; 39A06; fixed point theorem; Kneser solutions; oscillation; Third-order dynamic equation; time scales
International Standard Serial Number (ISSN)
1303-6149; 1300-0098
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Scientific and Technological Research Council of Turkiye (Tubitak), All rights reserved.
Publication Date
01 Jan 2025
