一类广义边值传递问题的Green函数
Green's Function of a generalized boundary value transmission problem
摘要：
本文研究了Sturm-Liouville方程在两个区间上的广义边值传递问题。在直和空间$L_{2}[a,c)\oplus L_{2}(c,b]\oplus\mathbb{C}^{2}$中引入修正的内积，并在其中定义对称线性算子，使得所考虑的问题可以解释为该算子的本征值问题.然后通过提出一种新的方法，构造出所考虑问题的格林函数，并求出相应非齐次问题的预解函数。
英文摘要：
The aim of this study is to investigate a class of generalized boundary value transmission problems (BVTP's) for Sturm-Liouville equation on two separate intervals. We introduce modified inner product in direct sum space $L_{2}[a,c)\oplus L_{2}(c,b]\oplus\mathbb{C}^{2}$ and define symmetric linear operator in it such a way that the considered problem can be interpreted as an eigenvalue problem of this operator. Then by suggesting an own approaches we construct Green's function for problem under consideration and find the resolvent function for corresponding inhomogeneous problem.
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