# Show that for a regular S-L system, if q(t) is increased to q1(t) > q(t), each nth eigenvalue of the new system is larger than that of the old.

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