具有第一类奇异性的线性常微分方程组射线上边值问题解的解的积分表示
The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind
摘要：
考虑一类非齐次线性常微分方程组的无穷远消失$C^1([0,\oo))$ -解问题，该方程组的一阶极点在$x=0$ .共振的情况下，相应的齐次问题有非平凡的解决方案是主要的兴趣。在齐次系统在$[1,\oo)$上指数二分且系统算子在$x=0$上的留数不具有实部为1的特征值的条件下，构造了广义格林函数.我们还建立了条件下，主要的非齐次问题可以减少到诺特一个非零指标。
英文摘要：
We consider a problem of finding vanishing at infinity $C^1([0,\oo))$-solutions to non-homogeneous system of linear ODEs which has the pole of first order at $x=0$. The resonant case where the corresponding homogeneous problem has nontrivial solutions is of main interest. Under the conditions that the homogeneous system is exponentially dichotomic on $[1,\oo)$ and the residue of system's operator at $x=0$ does not have eigenvalues with real part 1, we construct the so called generalized Green function. We also establish conditions under which the main non-homogeneous problem can be reduced to the Noetherian one with nonzero index.
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