Existence of positive periodic solutions for a class of second-order neutral functional differential equations
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He Yang
and
Lu Zhang
Abstract
In this paper, under some ordered conditions, we investigate the existence of positive ω-periodic solutions for a class of second-order neutral functional differential equations with delayed derivative in nonlinearity of the form (x(t) − cx(t − δ))″ + a(t)g(x(t))x(t) = λb(t)f(t, x(t), x(t − τ 1(t)), x′(t − τ 2(t))). By utilizing the perturbation method of a positive operator and the fixed point index theory in cones, some sufficient conditions are established for the existence as well as the non-existence of positive ω-periodic solutions.
Funding source: The National Natural Science Function of China
Award Identifier / Grant number: 11701457
Acknowledgements
The authors thanks the referees and editors for their careful reading of the manuscript and valuable comments, which helped us to improve the quality of the paper.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The research is supported by the National Natural Science Function of China (No. 11701457).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Research on bifurcation and chaos characteristics of planet gear transmission system with mixed elastohydrodynamic lubrication (EHL) friction
- Nonlinear modeling and simulation of flywheel energy storage rotor system with looseness and rub-impact coupling hitch
- Application of the piecewise constant method in nonlinear dynamics of drill string
- Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti–Rabinowitz condition
- A stabilized fractional-step finite element method for the time-dependent Navier–Stokes equations
- Self-adaptive inertial subgradient extragradient scheme for pseudomonotone variational inequality problem
- An accurate and novel numerical simulation with convergence analysis for nonlinear partial differential equations of Burgers–Fisher type arising in applied sciences
- Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method
- N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions
- Quintic B-spline collocation method for the numerical solution of the Bona–Smith family of Boussinesq equation type
- Existence of positive periodic solutions for a class of second-order neutral functional differential equations
