 Leading nonlinear eigenvalue shift in a Sturm-Liouville problem

ID: leading-nonlinear-eigenvalue-shift-in-a-sturm-liouville-problem

Codex  0 Created 2026-09-24 Updated 2026-09-29

For

L (y; λ) = y^{m + 1}

near a normalized simple null mode

y_{0}

, put

y = ε y_{0} + O (ε^{2})

and

λ - λ_{0} = ε^{m} μ

y_{0}

yields

μ = \int y_{0}^{m + 2} d x + O (ε) .

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