From nonlinear Schr\"odinger equation to interacting particle system: 1 < p < 2
Abstract
We investigate the limiting behavior of solutions with infinitely many peaks to nonlinear Schr\"odinger equations [-epsilon2 Delta uepsilon + uepsilon = uepsilonp, uepsilon > 0 in Rn,] as epsilon -> 0, where p is Sobolev subcritical. We derive the interaction law among the limiting peak points and complete the analysis for the previously unresolved range 1 < p < 2, extending the work of Ao, Lv, and Wang (J. Differential Equations, 2025).
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