Makale detayı · 2025
Nonoscillatory solutions of third-order nonlinear dynamic equations: Existence and nonexistence
Turkish Journal of Mathematics
- Yıl
- 2025
- ISSN
1300-0098- Tür
- article
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Özet
İngilizce (OpenAlex)
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.
Konular
- Nonlinear Differential Equations Analysis
- Differential Equations and Numerical Methods
- Advanced Mathematical Physics Problems
Birincil konu Nonlinear Differential Equations Analysis