Nonoscillatory Solutions for <i>m</i>-th-Order Nonlinear Neutral Differential Equations with General Delays: Fixed-Point Approach and Application
This paper investigates the existence and uniqueness of bounded nonoscillatory solutions for two classes of <i>m</i>-th-order nonlinear neutral differential equations that incorporate both discrete and distributed delays. By applying Banach’s fixed-point theorem, we establish sufficient...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/15/2362 |
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| Summary: | This paper investigates the existence and uniqueness of bounded nonoscillatory solutions for two classes of <i>m</i>-th-order nonlinear neutral differential equations that incorporate both discrete and distributed delays. By applying Banach’s fixed-point theorem, we establish sufficient conditions under which such solutions exist. The results extend and generalize previous works by relaxing assumptions on the nonlinear terms and accommodating a wider range of feedback structures, including positive, negative, bounded, and unbounded cases. The mathematical framework is unified and applicable to a broad class of problems, providing a comprehensive treatment of neutral equations beyond the first or second order. To demonstrate the practical relevance of the theoretical findings, we analyze a delayed temperature control system as an application and provide numerical simulations to illustrate nonoscillatory behavior. This paper concludes with a discussion of analytical challenges, limitations of the numerical scope, and possible future directions involving stochastic effects and more complex delay structures. |
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| ISSN: | 2227-7390 |