Existence of multiple solutions to a discrete fourth order periodic boundary value problem
Existence of multiple solutions to a discrete fourth order periodic boundary value problem
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DOI：
10.3934/proc.2013.2013.291
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
J. Graef;L. Kong;Min Wang
中科院分区：
文献类型：
--
作者：
J. Graef;L. Kong;Min Wang
得到了离散四阶周期边值问题\开始{equation*} \开始{array}{l}\Delta ^4 u（t-2）-\Delta（p（t-1）\Delta u（t-1））+q（t）u（t）=f（t，u（t）），\quad t\in [1，N]_{\mathbb{Z}}，\\Delta^iu（-1）=\Delta^iu（N-1），\quad i=0，1，2，3多解存在的充分条件. \end{array} \end{equation*}我们的分析主要基于变分法和临界点理论。最后给出了一个算例来说明结果。
Sufficient conditions are obtained for the existence of multiple solutions to the discrete fourth order periodic boundary value problem \begin{equation*} \begin{array}{l} \Delta^4 u(t-2)-\Delta(p(t-1)\Delta u(t-1))+q(t) u(t)=f(t,u(t)),\quad t\in [1,N]_{\mathbb{Z}},\\ \Delta^iu(-1)=\Delta^iu(N-1),\quad i=0, 1,2, 3. \end{array} \end{equation*} Our analysis is mainly based on the variational method and critical point theory. One example is included to illustrate the result.