Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters

The author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u,  0<t<1,  t≠tk,  Δu|t=tk=μIktk,  utk,  Δu′|t=tk=0,  k=1,2,…,n,  au(0)-bu′(0)=∫01‍g(t)u(t)dt,u′(1)=0, where λ>0 and μ>0 are two parameters. Using fixed point theories, se...

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Main Author: Meiqiang Feng
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/534787
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author Meiqiang Feng
author_facet Meiqiang Feng
author_sort Meiqiang Feng
collection DOAJ
description The author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u,  0<t<1,  t≠tk,  Δu|t=tk=μIktk,  utk,  Δu′|t=tk=0,  k=1,2,…,n,  au(0)-bu′(0)=∫01‍g(t)u(t)dt,u′(1)=0, where λ>0 and μ>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 λ>0 and μ>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 Ding and Wang.
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spelling doaj-art-23e7a2c2bd604e688319a1609bf418ab2025-08-20T02:04:13ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/534787534787Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two ParametersMeiqiang Feng0School of Applied Science, Beijing Information Science & Technology University, Beijing, 100192, ChinaThe author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u,  0<t<1,  t≠tk,  Δu|t=tk=μIktk,  utk,  Δu′|t=tk=0,  k=1,2,…,n,  au(0)-bu′(0)=∫01‍g(t)u(t)dt,u′(1)=0, where λ>0 and μ>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 λ>0 and μ>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 Ding and Wang.http://dx.doi.org/10.1155/2014/534787
spellingShingle Meiqiang Feng
Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
Abstract and Applied Analysis
title Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
title_full Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
title_fullStr Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
title_full_unstemmed Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
title_short Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
title_sort positive solutions for a second order p laplacian boundary value problem with impulsive effects and two parameters
url http://dx.doi.org/10.1155/2014/534787
work_keys_str_mv AT meiqiangfeng positivesolutionsforasecondorderplaplacianboundaryvalueproblemwithimpulsiveeffectsandtwoparameters