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Non-degeneracy and Uniqueness of Periodic Solutions for a Liénard Equation with a Linear Difference Operator

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  1. Article

    Open Access

    Hopf bifurcation in an age-structured predator–prey system with Beddington–DeAngelis functional response and constant harvesting

    In this paper, an age-structured predator–prey system with Beddington–DeAngelis (B–D) type functional response, prey refuge and harvesting is investigated, where the predator fertility function f(a) and the matur...

    San-**ng Wu, Zhi-Cheng Wang, Shigui Ruan in Journal of Mathematical Biology (2024)

  2. Article

    Open Access

    Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition

    We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral...

    Weiwei Zhao, **aoling Shao, Changhui Hu, Zhiyu Cheng in Boundary Value Problems (2024)

  3. Article

    Open Access

    Boundary value problems of quaternion-valued differential equations: solvability and Green’s function

    This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs). Employing the theory of quaternionic matrice...

    Jie Liu, Siyu Sun, Zhibo Cheng in Boundary Value Problems (2023)

  4. Article

    Open Access

    Positive periodic solution for prescribed mean curvature generalized Liénard equation with a singularity

    The main purpose of this paper is to investigate the existence of a positive periodic solution for a prescribed mean curvature generalized Liénard equation with a singularity (weak and strong singularities of ...

    Yun **n, Zhibo Cheng in Boundary Value Problems (2020)

  5. Article

    Open Access

    Periodic solutions for p-Laplacian neutral differential equation with multiple delay and variable coefficients

    In this paper, we first discuss some properties of the neutral operator with multiple delays and variable coefficients ...

    Zhonghua Bi, Zhibo Cheng, Shaowen Yao in Advances in Difference Equations (2019)

  6. Article

    Open Access

    Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type

    In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, ...

    Yun **n, Hongmin Liu, Zhibo Cheng in Journal of Inequalities and Applications (2018)

  7. Article

    Open Access

    Periodic solution for p-Laplacian Rayleigh equation with attractive singularity and time-dependent deviating argument

    In this paper, we consider a p-Laplacian singular Rayleigh equation with time-dependent deviating argument ...

    Zhibo Cheng, Zhonghua Bi, Shaowen Yao in Boundary Value Problems (2018)

  8. Article

    Open Access

    Positive periodic solution for higher-order p-Laplacian neutral singular Rayleigh equation with variable coefficient

    In this paper, we consider the existence of a positive periodic solution for the following kind of high-order p-Laplacian neutral singular Rayleigh equation with variable coefficient:

    Yun **n, Shaowen Yao, Zhibo Cheng in Boundary Value Problems (2017)

  9. Article

    Open Access

    Study on a kind of ϕ-Laplacian Liénard equation with attractive and repulsive singularities

    In this paper, by application of the Manasevich-Mawhin continuation theorem, we investigate the existence of a positive periodic solution for a kind of ϕ-Laplacian singular Liénard equation with attractive and re...

    Yun **n, Zhibo Cheng in Journal of Inequalities and Applications (2017)

  10. Article

    Open Access

    Study on a kind of neutral Rayleigh equation with singularity

    In this paper, we consider a kind of neutral Rayleigh equation with singularity, ...

    Yun **n, Zhibo Cheng in Boundary Value Problems (2017)

  11. Article

    Open Access

    New results for Brillouin electron beam focusing system

    An experimental conjecture on the existence of positive periodic solutions for the Brillouin electron beam focusing system ...

    Zhibo Cheng, Shaowen Yao in Boundary Value Problems (2017)

  12. Article

    Open Access

    Study on a kind of fourth-order p-Laplacian Rayleigh equation with linear autonomous difference operator

    In this paper, we consider the following fourth-order Rayleigh type p-Laplacian generalized neutral differential equation with linear autonomous difference operator:

    Yun **n, Xuefeng Han, Zhibo Cheng in Boundary Value Problems (2017)

  13. Article

    Open Access

    Positive periodic solution for ϕ-Laplacian Rayleigh equation with strong singularity

    In this paper, we discuss a kind of ϕ-Laplacian Rayleigh equation with strong singularity

    Yun **n, Zhibo Cheng in Boundary Value Problems (2016)

  14. Article

    Open Access

    Positive periodic solution for high-order p-Laplacian neutral differential equation with singularity

    In this paper, we consider the following high-order p-Laplacian neutral differential equation with singularity: ...

    Yun **n, Xuefeng Han, Zhibo Cheng in Boundary Value Problems (2016)

  15. Article

    Open Access

    Positive periodic solution of p-Laplacian Liénard type differential equation with singularity and deviating argument

    In this paper, we consider the following p-Laplacian Liénard type differential equation with singularity and deviating argument: ...

    Yun **n, Zhibo Cheng in Advances in Difference Equations (2016)

  16. Article

    Open Access

    Some results for fourth-order nonlinear differential equation with singularity

    By application of Green’s function and some fixed point theorems, i.e., Leray-Schauder alternative principle and Schauder’s fixed point theorem, we establish two new existence results of positive periodic solutio...

    Yun **n, Zhibo Cheng in Boundary Value Problems (2015)

  17. Article

    Open Access

    Existence and uniqueness of positive periodic solution for ϕ-Laplacian Liénard equation

    By applying the Manásevich-Mawhin continuation theorem, we establish some sufficient conditions for the existence and uniqueness of positive periodic solutions for the Liénard type ϕ-Laplacian operator equation.

    Yun **n, Xuefeng Han, Zhibo Cheng in Boundary Value Problems (2014)

  18. Article

    Open Access

    Neutral operator with variable parameter and third-order neutral differential equation

    In this article, we discuss the properties of the neutral operator with variable parameter ...

    Yun **n, Zhibo Cheng in Advances in Difference Equations (2014)

  19. Article

    Open Access

    Existence and uniqueness of a positive periodic solution for Rayleigh type ϕ-Laplacian equation

    By using the Manásevich-Mawhin continuation theorem and some analysis skills, we establish some sufficient condition for the existence and uniqueness of positive T-periodic solutions for a generalized Rayleigh ty...

    Yun **n, Zhibo Cheng in Advances in Difference Equations (2014)

  20. Article

    Open Access

    Existence of positive periodic solutions for third-order differential equation with strong singularity

    Sufficient conditions are presented for the existence of positive periodic solutions for a third-order nonlinear differential equation with singularity. Besides, an example is given to illustrate the results.

    Zhibo Cheng in Advances in Difference Equations (2014)

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