Consider the S-L equation $$\frac{d}{d t}\left[p(t) \frac{d u}{d t}\right]+[\lambda r(t)-q(t)] u=0$$ Show that for a regular S-L system, if $q(t)$ is increased to $q_{1}(t)>q(t),$ each $n$ th eigenvalue of the new system is larger than that of the old.

Can someone please show me how to prove this?

Thank you


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