论文标题
多点边界值问题的近似属性
Approximation properties of multipoint boundary-value problems
论文作者
论文摘要
我们考虑了$ r $ $ - 订购普通微分方程的系统的一系列线性边界值问题，其解决方案范围比$ n \ geq r $ times连续微分函数$ y：[a，b] \ to \ to \ mathbb {c} c}^{m} $。这些问题的边界条件是最通用的形式$ by = q $，其中$ b $是任意连续的线性运算符，从$（c^{（n）}）^{m} $到$ \ MATHBB {C}^{RM} $。我们通过解决某些多点边界值问题的解决方案来证明，可以在$（c^{（n）}）^m $中近似于所考虑的问题的解决方案。后一个问题不取决于所考虑的问题的右侧，并且是明确构建的。
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable functions $y:[a,b]\to\mathbb{C}^{m}$. The boundary conditions for these problems are of the most general form $By=q$, where $B$ is an arbitrary continuous linear operator from $(C^{(n)})^{m}$ to $\mathbb{C}^{rm}$. We prove that the solutions to the considered problems can be approximated in $(C^{(n)})^m$ by solutions to some multipoint boundary-value problems. The latter problems do not depend on the right-hand sides of the considered problem and are built explicitly.
