论文标题
n阶方程的解决方案的第n阶边界值问题具有积分边界条件
Solutions of the Variational Equation for an nth Order Boundary Value Problem with an Integral Boundary Condition
论文作者
论文摘要
在本文中，我们讨论了解决边界价值问题的解决方案$ y^{（n）} = f（x，y，y，y^{'}，y^{''}，\ ldots，y^{（n-1）}），\; a <x <b，\; y^{（i）}（x_j）= y_ {ij}，\; 0 \ leq i \ leq m_j，\; 1 \ leq j \ leq k-1 $和$ y^{（i）}（x_k） + \ int_c^d p y（x）\; dx = y_ {ik {ik}，\; 0 \ leq i \ leq i \ leq i \ leq m_k，\;我们表明，在某些条件下，存在相对于各种边界数据的边界值问题解决方案$ y（x）的部分衍生物，并沿$ y（x）$求解了相关的变分方程。
In this paper, we discuss differentiation of solutions to the boundary value problem $y^{(n)} = f(x, y, y^{'}, y^{''}, \ldots, y^{(n-1)}), \; a<x<b,\; y^{(i)}(x_j) = y_{ij},\; 0\leq i \leq m_j, \; 1 \leq j \leq k-1$, and $y^{(i)}(x_k) + \int_c^d p y(x)\;dx = y_{ik}, \;0 \leq i \leq m_k,\;\sum_{i=1}^km_i=n$ with respect to the boundary data. We show that under certain conditions, partial derivatives of the solution $y(x)$ of the boundary value problem with respect to the various boundary data exist and solve the associated variational equation along $y(x)$.
