Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem
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DOI：
10.1007/s00033-012-0243-7
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发表时间：
2012-07
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影响因子：
--
通讯作者：
Ruyun Ma;Chenghua Gao
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文献类型：
--
作者：
Ruyun Ma;Chenghua Gao
取一个t≥4的整数。本文给出了不一定线性化的四阶非线性差分方程$$\begin{array}{lll}\Delta^4 u(t-2)&=&f(t,u(t),\Delta^2u(t-1)),\quad t\in \{2,\ldots, T\},\\u(0)=&u(T+2)=\Delta^2u(0)=\Delta^2u(T)=0,\end{array}$$边值问题正解分支的全局描述。我们的方法基于Krein-Rutman定理、拓扑度理论和全局分岔技术。
Letbe an integer withT≥ 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.