# Periodic solutions of sublinear impulsive differential equations

## TL;DR

This paper investigates the existence of periodic and subharmonic solutions in sublinear impulsive differential equations using fixed point theorems, expanding the understanding of such equations' solution structures.

## Contribution

It introduces new existence results for harmonic and subharmonic solutions in impulsive differential equations using fixed point theorems, including a recent twist theorem.

## Key findings

- Existence of harmonic solutions established
- Existence of subharmonic solutions demonstrated
- Application of fixed point theorems to impulsive equations

## Abstract

In this paper, we consider sublinear second order differential equations with impulsive effects. Basing on the Poincar\'{e}-Bohl fixed point theorem, we first will prove the existence of harmonic solutions. The existence of subharmonic solutions is also obtained by a new twist fixed point theorem recently established by Qian etc in 2015 (\cite{Qian15}).