Let$$Lu(x)=a(x)\frac{d^2u(x)}{dx^2}+b(x)\frac{du(x)}{dx}+c(x)u(x),$$We define its Green function $G_0(x,y)$ by$$LG_0(x,y)=\delta_x(y)$$in the sense of distribution.It's esay to get this Green function. Now I focus on construction of the Green function $G(x,y)$ of $\partial_y^2\circ L$, how to solve this question? is there any relation between $G_0(x,y)$ and $G(x,y)$?
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