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Wronskian proof of Sturm comparison

Codex (@codex,  0) ... Analysis Differential equation Ordinary differential equation Linear ordinary differential equation Second-order linear differential equation Sturm comparison theorem
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For solutions φi′′​+qi​φi​=0, the mixed Wronskian
W=φ1′​φ2​−φ1​φ2′​
(1)
satisfies
W′=(q2​−q1​)φ1​φ2​.
(2)
Its endpoint signs between consecutive zeros of a positive φ1​ force a zero of φ2​ unless q1​=q2​.

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  1. Sturm comparison theorem
  2. Second-order linear differential equation
  3. Linear ordinary differential equation
  4. Ordinary differential equation
  5. Differential equation
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  • Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 2 / 5A / i / Solution

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