 Singular homogeneous solution of the Lane-Emden equation

ID: singular-homogeneous-solution-of-the-lane-emden-equation

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

When

a = 2/ (p - 1)

and

a < d - 2

, the Lane-Emden equation has the singular scale-invariant solution

u_{\infty} (r) = (a (d - 2 - a))^{1/ (p - 1)} r^{- a} .

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