Sharp Stability of $\Delta u-u+|u|^{p-1}u$ near a finite sums of ground states

TL;DR

This paper provides precise stability estimates for solutions near finite sums of ground states in a nonlinear PDE, with results tailored to the dimension and nonlinearity order.

Contribution

It introduces sharp quantitative stability estimates for finite sums of ground states, considering the influence of dimension and nonlinearity.

Findings

Stability estimates depend sharply on dimension and nonlinearity.

Results apply to solutions close to finite sums of ground states.

The estimates are optimal in a quantitative sense.

Abstract

We establish sharp quantitative stability estimates near finite sums of ground states. The results depend on the dimension and the order of nonlinearity.