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Wronskian proof of Sturm comparison
...
Analysis
Differential equation
Ordinary differential equation
Linear ordinary differential equation
Second-order linear differential equation
Sturm comparison theorem
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Words: 28
For solutions
φ
i
′′
+
q
i
φ
i
=
0
, the mixed Wronskian
W
=
φ
1
′
φ
2
−
φ
1
φ
2
′
(288)
satisfies
W
′
=
(
q
2
−
q
1
)
φ
1
φ
2
.
(289)
Its endpoint signs between consecutive zeros of a positive
φ
1
force a zero of
φ
2
unless
q
1
=
q
2
.
Ancestors
(9)
Sturm comparison theorem
Second-order linear differential equation
Linear ordinary differential equation
Ordinary differential equation
Differential equation
Analysis
Area of mathematics
Mathematics
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