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Global bifurcation of positive solutions for discrete Kirchhoff equations.

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Titel: Global bifurcation of positive solutions for discrete Kirchhoff equations.
Autoren: Shi, Xuanrong1 (AUTHOR) sxr15209336785@163.com, Lei, Xiangbing1 (AUTHOR)
Quelle: Dynamical Systems: An International Journal. Sep2025, Vol. 40 Issue 3, p541-554. 14p.
Schlagwörter: BIFURCATION theory, BOUNDARY value problems, SMOOTHNESS of functions
Abstract: In this paper, we show the global structure of positive solutions for the boundary value problem \[ \left\{\begin{array}{lc} \displaystyle-A\left(\sum_{m=1}^{T+1}(D u)(m-1)^2\right)(D^{2}u)(k-1)=\lambda f(k,u(k)), & k\in \mathbb{T}, \\ u(0)=u(T+1)=0, & \\ \end{array} \right. \] { − A (∑ m = 1 T + 1 (Du) (m − 1) 2) (D 2 u) (k − 1) = λf (k , u (k)) , k ∈ T , u (0) = u (T + 1) = 0 , where $ \lambda \gt 0 $ λ > 0 is a parameter, $ \mathbb {T}:=\{1,\ldots,T\} $ T := { 1 , ... , T } , $ A(t):\mathbb {R}^{+}\rightarrow \mathbb {R}^{+} $ A (t) : R + → R + , $ f(k,u): \mathbb {T}\times \mathbb {R}\rightarrow \mathbb {R} $ f (k , u) : T × R → R are continuous functions. Depending on the assumption of A and the behaviour of f near 0 and ∞, we obtain the existence and multiplicity results of positive solutions. The proof of our main results is based on the bifurcation techniques. [ABSTRACT FROM AUTHOR]
Copyright of Dynamical Systems: An International Journal is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Global bifurcation of positive solutions for discrete Kirchhoff equations.
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  Data: <searchLink fieldCode="JN" term="%22Dynamical+Systems%3A+An+International+Journal%22">Dynamical Systems: An International Journal</searchLink>. Sep2025, Vol. 40 Issue 3, p541-554. 14p.
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  Data: <searchLink fieldCode="DE" term="%22BIFURCATION+theory%22">BIFURCATION theory</searchLink><br /><searchLink fieldCode="DE" term="%22BOUNDARY+value+problems%22">BOUNDARY value problems</searchLink><br /><searchLink fieldCode="DE" term="%22SMOOTHNESS+of+functions%22">SMOOTHNESS of functions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we show the global structure of positive solutions for the boundary value problem \[ \left\{\begin{array}{lc} \displaystyle-A\left(\sum_{m=1}^{T+1}(D u)(m-1)^2\right)(D^{2}u)(k-1)=\lambda f(k,u(k)), & k\in \mathbb{T}, \\ u(0)=u(T+1)=0, & \\ \end{array} \right. \] { − A (∑ m = 1 T + 1 (Du) (m − 1) 2) (D 2 u) (k − 1) = λf (k , u (k)) , k ∈ T , u (0) = u (T + 1) = 0 , where $ \lambda \gt 0 $ λ > 0 is a parameter, $ \mathbb {T}:=\{1,\ldots,T\} $ T := { 1 , ... , T } , $ A(t):\mathbb {R}^{+}\rightarrow \mathbb {R}^{+} $ A (t) : R + → R + , $ f(k,u): \mathbb {T}\times \mathbb {R}\rightarrow \mathbb {R} $ f (k , u) : T × R → R are continuous functions. Depending on the assumption of A and the behaviour of f near 0 and ∞, we obtain the existence and multiplicity results of positive solutions. The proof of our main results is based on the bifurcation techniques. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Dynamical Systems: An International Journal is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/14689367.2025.2503192
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 541
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      – SubjectFull: BIFURCATION theory
        Type: general
      – SubjectFull: BOUNDARY value problems
        Type: general
      – SubjectFull: SMOOTHNESS of functions
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      – TitleFull: Global bifurcation of positive solutions for discrete Kirchhoff equations.
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              M: 09
              Text: Sep2025
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              Y: 2025
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