Bibliographic Details
| Title: |
Global bifurcation of positive solutions for discrete Kirchhoff equations. |
| Authors: |
Shi, Xuanrong1 (AUTHOR) sxr15209336785@163.com, Lei, Xiangbing1 (AUTHOR) |
| Source: |
Dynamical Systems: An International Journal. Sep2025, Vol. 40 Issue 3, p541-554. 14p. |
| Subject Terms: |
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.) |
| Database: |
Business Source Index |
Full Text Finder 
Nájsť tento článok vo Web of Science