Existence of nonoscillatory solutions for higher order nonlinear mixed neutral differential equations

Hui Li; Nana Jin; Yu Zhang; Hui Li; Nana Jin; Yu Zhang

doi:10.3934/mmc.2024033

Mathematical Modelling and Control

2024, Volume 4, Issue 4: 417-423. doi: 10.3934/mmc.2024033

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Research article

Existence of nonoscillatory solutions for higher order nonlinear mixed neutral differential equations

School of Mathematical Sciences, University of Ji'nan, Ji'nan 250022, China

Received: 17 June 2024 Revised: 25 July 2024 Accepted: 02 August 2024 Published: 25 November 2024

In this paper, the existence of nonoscillatory solutions for a class of higher-order nonlinear differential equations is investigated. Notably, the equations are of mixed neutral type with a forcing term, which distinguished the equations in this paper from the existing ones and made the qualitative analysis of the solution more complicated. By means of the Schauder-Tychonoff fixed point theorem and inequality techniques, some new sufficient conditions for the existence of nonoscillatory solutions were established. The results in this paper improved and generalized some known results in the existing works. Finally, an example was given to illustrate the effectiveness of the proposed method.
- nonoscillatory solutions,
- neutral,
- mixed differential equations,
- nonlinear analysis
Citation: Hui Li, Nana Jin, Yu Zhang. Existence of nonoscillatory solutions for higher order nonlinear mixed neutral differential equations[J]. Mathematical Modelling and Control, 2024, 4(4): 417-423. doi: 10.3934/mmc.2024033

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Abstract

In this paper, the existence of nonoscillatory solutions for a class of higher-order nonlinear differential equations is investigated. Notably, the equations are of mixed neutral type with a forcing term, which distinguished the equations in this paper from the existing ones and made the qualitative analysis of the solution more complicated. By means of the Schauder-Tychonoff fixed point theorem and inequality techniques, some new sufficient conditions for the existence of nonoscillatory solutions were established. The results in this paper improved and generalized some known results in the existing works. Finally, an example was given to illustrate the effectiveness of the proposed method.

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