离散边值问题的非伪解的变分方法
Non-spurious solutions to discrete boundary value problems through variational methods
摘要：
利用直接变分方法，我们考虑了狄利克雷问题$\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $，$x\left( 0\right) =x\left( 1\right) =0 $的非伪解的存在性，其中$f:\left[ 0,1\right] \times \mathbb{R} \rightarrow \mathbb{R}$是在$x$中凸的联合连续函数，它不需要满足任何进一步的增长条件.
英文摘要：
Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[ 0,1\right] \times \mathbb{R} \rightarrow \mathbb{R}$ is a jointly continuous function convex in $x$ which does not need to satisfy any further growth conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
