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...
Saved in:
| Main Authors: | , |
|---|---|
| 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!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |