Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and  η∈(0,1), where Dα is the standard Riemann-Liouville derivat...

Full description

Saved in:
Bibliographic Details
Main Authors: Zhaocai Hao, Yubo Huang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/158436
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832549863995211776
author Zhaocai Hao
Yubo Huang
author_facet Zhaocai Hao
Yubo Huang
author_sort Zhaocai Hao
collection DOAJ
description We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and  η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.
format Article
id doaj-art-80a7ec9ba9f64a0ab18640066cb20784
institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-80a7ec9ba9f64a0ab18640066cb207842025-02-03T06:08:25ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/158436158436Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced ArgumentsZhaocai Hao0Yubo Huang1School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, ChinaWe discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and  η∈(0,1), where Dα is the standard Riemann-Liouville derivative, f:[0,∞)→[0,∞) is continuous, f(0)>0, h :[0,1]→(−∞,+∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.http://dx.doi.org/10.1155/2014/158436
spellingShingle Zhaocai Hao
Yubo Huang
Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
Abstract and Applied Analysis
title Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
title_full Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
title_fullStr Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
title_full_unstemmed Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
title_short Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments
title_sort existence of positive solutions to nonlinear fractional boundary value problem with changing sign nonlinearity and advanced arguments
url http://dx.doi.org/10.1155/2014/158436
work_keys_str_mv AT zhaocaihao existenceofpositivesolutionstononlinearfractionalboundaryvalueproblemwithchangingsignnonlinearityandadvancedarguments
AT yubohuang existenceofpositivesolutionstononlinearfractionalboundaryvalueproblemwithchangingsignnonlinearityandadvancedarguments