Instability of bound states for abstract nonlinear Schr\"{o}dinger equations

TL;DR

This paper investigates the instability of bound states in abstract nonlinear Schrödinger equations, establishing a new borderline instability result and providing unified proofs of existing results.

Contribution

It introduces a novel instability criterion for borderline cases and unifies previous results through a comprehensive approach.

Findings

Established a new instability result for borderline cases.

Reproved known results using a unified method.

Enhanced understanding of stability criteria for nonlinear Schrödinger equations.

Abstract

We study the instability of bound states for abstract nonlinear Schr\"{o}dinger equations. We prove a new instability result for a borderline case between stability and instability. We also reprove some known results in a unified way.