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Distribution solutions of a static dispersion Schr\"{o}dinger equation

math.AP · 2026-07-07 · accept · novelty 5.0

Positive distribution solutions of $-Δu + a²Δ²u = u^q$ in ℝ³ exist only for q>5, super-solutions only for q>3, and all such solutions are radial, differentiable, and decay like the Coulomb-type kernel $K_a(x)=(1-e^{-|x|/a})/|x|$.

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  • Distribution solutions of a static dispersion Schr\"{o}dinger equation math.AP · 2026-07-07 · accept · none · ref 2

    Positive distribution solutions of $-Δu + a²Δ²u = u^q$ in ℝ³ exist only for q>5, super-solutions only for q>3, and all such solutions are radial, differentiable, and decay like the Coulomb-type kernel $K_a(x)=(1-e^{-|x|/a})/|x|$.