AI 中文总结
研究Sobolev空间中带多点边界条件且含Caputo导数的线性常微分方程组边值问题，建立解关于参数在该空间中连续的构造性充分条件。
AI 中文摘要
研究了最一般类的任意阶r≥1线性常微分方程组的多点非齐次边值问题，其解属于给定的Sobolev空间W_p^{n+r}，其中n≥0且1≤p≤∞。这类问题的边界条件包含分数阶或整数阶的Caputo导数，其阶数可超过微分系统方程的阶数。建立了构造性充分条件，据此这些问题的解关于抽象度量空间中的参数在Sobolev空间W_p^{n+r}中连续。
英文摘要
The most general class of multipoint inhomogeneous boundary-value problems for systems of linear ordinary differential equations of arbitrary order $r\geq 1$ is investigated, whose solutions belong to a given Sobolev space $W_p^{n+r}$, where $n\geq 0$ and $1\leq p\leq \infty$. The boundary conditions in these problems contain Caputo derivatives of fractional or integer orders, which may exceed the order of the differential system equations. Constructive sufficient conditions are established under which the solutions of these problems are continuous with respect to a parameter from an abstract metric space in the Sobolev space $W_p^{n+r}$.
CommentsThis manuscript has been accepted for publication in the Complex Analysis and Operator Theory journal
