Positive solutions for a second-order \(p\)-Laplacian boundary value problem with impulsive effects and two parameters
type: Item
instance of: scholarly article
title: Positive solutions for a second-order \(p\)-Laplacian boundary value problem with impulsive effects and two parameters
zbMATH Open document ID: 1475.34024
DOI: 10.1155/2014/534787
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The author considers an impulsive boundary value problem involving the one-dimensional \(p\)-Laplacian \(-(\varphi_p(u'))'=\lambda w(t)f(t,u)\), \(0<t<1\), \(t\neq t_k\), \(\Delta u|_{t=t_k}=\mu I_k(t_k,u(t_k))\), \(\Delta u'|_{t=t_k}=0\), \(k=1,2,\dots,n\), \(au(0)-bu'(0)=\int^1_0g(t)u(t)dt,u'(1)=0\) where \(\lambda>0\) and \(\mu>0\) are two parameters. Using fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values of \(\lambda>0\) and \(\mu>0\). The exact upper and lower bounds for these positive solutions are also given. Moreover, the approach to deal with the impulsive term is different from earlier approaches. In this paper, our results cover equations without impulsive effects and are compared with some recent results by \textit{W. Ding} and \textit{Yu. Wang} [Commun. Nonlinear Sci. Numer. Simul. 18, No. 5, 1095--1105 (2013; Zbl 1263.34033)].
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B37
zbMATH DE Number: 7022568
Wikidata QID: Q59039221
author: Meiqiang Feng
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/534787
OpenAlex ID: W2059780942
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description: scientific article; zbMATH DE number 7022568