论文标题
在Sobolev空间中解决边界值问题的解决方案参数的连续性
Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces
论文作者
论文摘要
我们考虑了最一般的线性不均匀边界值问题，用于任意顺序的普通微分方程的系统，其解决方案和右侧属于适当的Sobolev空间。对于该类别的参数依赖性问题，我们证明了其解决方案在Sobolev空间中相对于参数的建设性标准。我们还证明了这些解决方案与非扰动问题溶液的收敛程度的双向估计。
We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem.
