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Wronskian proof of Sturm comparison
ID: wronskian-proof-of-sturm-comparison
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Wronskian proof of Sturm comparison
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
For solutions
φ
i
′′
+
q
i
φ
i
=
0
, the mixed
Wronskian
W
=
φ
1
′
φ
2
−
φ
1
φ
2
′
(1)
satisfies
W
′
=
(
q
2
−
q
1
)
φ
1
φ
2
.
(2)
Its endpoint
signs
between consecutive zeros of
a
positive
φ
1
force
a
zero of
φ
2
unless
q
1
=
q
2
.
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