Existence results for damped regular equations under periodic or Neumann boundary conditions
type: Item
instance of: scholarly article
title: Existence results for damped regular equations under periodic or Neumann boundary conditions
zbMATH Open document ID: 1497.34043
author: Feng Wang
author: Shengjun Li
author: Mirosława Zima
author: J. Ángel Cid
published in: Journal of Mathematical Analysis and Applications
publication date: 2022-02-14T00:00:00Z
review text: In this article, the authors state a version of the averaging and a method to construct lower and upper solutions in the reversed order that are suitable for both the periodic and the Neumann boundary conditions. As an application, they study the damped regular differential equation \[ \ddot{x}+c\dot{x}=\nu g(t)x^\lambda-h(t)x^\mu,\tag{1} \] where \(\lambda,\mu>0,\) \(g,h\in C([0,T]),\) \(c\in\mathbb{R}\) and \(\nu\) is a parameter. Indeed, under periodic conditions, that is \[ x(0)=x(T),\quad \dot{x}(0)=\dot{x}(T), \] or Neumann boundary conditions, i.e., \[ \dot{x}(0)=\dot{x}(T)=0, \] the existence of positive solutions of the equation (1) is investigated.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7472997
zbMATH Keywords: existence analysis
zbMATH Keywords: dynamic analysis
zbMATH Keywords: regular equations
zbMATH Keywords: periodic solutions
reviewed by: S. Shokooh
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125978
OpenAlex ID: W4200430306
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DOI: 10.1016/J.JMAA.2021.125978
description: scientific article; zbMATH DE number 7472997