Dear all, how can I transfer the following general Sturm-Liouville equation
$\displaystyle [p(x)y']'+[q(x)+\lambda r(x)]y=0$
into the following special Sturm-Liouville equation
$\displaystyle y''+(\lambda +q(x))y=0?$
Thank you very much.
Dear all, how can I transfer the following general Sturm-Liouville equation
$\displaystyle [p(x)y']'+[q(x)+\lambda r(x)]y=0$
into the following special Sturm-Liouville equation
$\displaystyle y''+(\lambda +q(x))y=0?$
Thank you very much.
There are some hints to the problem. It goes as follows.
1. Take $\displaystyle y=u(x)z$, choose appropriate $\displaystyle u(x)$, we can get $\displaystyle \ddot z+A(x)z=0$.
2. Then take $\displaystyle x=f(t)$ for some function $\displaystyle f$, we can see the result.
However, I could not check the second hint.