# Orbital stability of standing waves for Schr\"{o}dinger type equations with slowly decaying linear potential

## TL;DR

This paper investigates the existence and orbital stability of standing waves in Schrödinger equations with slowly decaying potentials, using advanced mathematical tools to cover subcritical and critical cases.

## Contribution

It provides a systematic analysis of standing wave stability for Schrödinger equations with slowly decaying potentials, employing concentration compactness, Gagliardo-Nirenberg inequalities, and refined operator estimates.

## Key findings

- Existence of standing waves established
- Orbital stability proven in subcritical and critical cases
- Methodology applicable to various nonlinearities

## Abstract

In this paper, kinds of Schr\"{o}dinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentration compactness principle, the sharp Gagliardo-Nirenberg inequality and a refined estimate of the linear operator, the existence and orbital stability of standing waves in $L^2$-subcritical and $L^2$-critical cases are established in a systematic way.