Abstract

Let \({T \in \mathbb{N}}\) be an integer with T ≥ 4. We give a global description of the branches of positive solutions of the nonlinear boundary value problem of fourth-order difference equation of the form $$\begin{array}{lll}\Delta^4 u(t-2)&=&f(t,u(t),\Delta^2u(t-1)),\quad t\in \{2,\ldots, T\},\\u(0)=&u(T+2)=\Delta^2u(0)=\Delta^2u(T)=0,\end{array}$$ that is not necessarily linearizable. Our approach is based on Krein–Rutman theorem, topological degree theory, and global bifurcation techniques.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.