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A Note on the Periodic Solutions for a Class of Third Order Differential Equations
Article

Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
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Author to whom correspondence should be addressed.
Academic Editor: Miguel Ángel López Guerrero
Symmetry 2021, 13(3), 449; https://doi.org/10.3390/sym13030449
Received: 27 February 2021 / Revised: 5 March 2021 / Accepted: 5 March 2021 / Published: 10 March 2021
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems)
This paper deals with the existence of ω-periodic solutions for nth-order ordinary differential equation involving fixed delay in Banach space E. Lnu(t)=f(t,u(t),u(tτ)),tR, where Lnu(t):=u(n)(t)+i=0n1aiu(i)(t), aiR, i=0,1,,n1, are constants, f(t,x,y):R×E×EE is continuous and ω-periodic with respect to t, τ>0. By applying the approach of upper and lower solutions and the monotone iterative technique, some existence and uniqueness theorems are proved under essential conditions. View Full-Text
Keywords: nth-order ordinary differential equations; delay; ω-periodic solutions; the measure of noncompactness; upper and lower solutions nth-order ordinary differential equations; delay; ω-periodic solutions; the measure of noncompactness; upper and lower solutions
MDPI and ACS Style

Yang, H.; Li, Y. Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces. Symmetry 2021, 13, 449. https://doi.org/10.3390/sym13030449

AMA Style

Yang H, Li Y. Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces. Symmetry. 2021; 13(3):449. https://doi.org/10.3390/sym13030449

Chicago/Turabian Style

Yang, He, and Yongxiang Li. 2021. "Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces" Symmetry 13, no. 3: 449. https://doi.org/10.3390/sym13030449

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