Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem
We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem u′′′(t)+λg(t)f(u(t))=0, 0<t<1, u(0)=αu(η), u′(0)=u′′(1)=0, where 0<η<1, 0<α<1, λ is a positive parameter, g:(0,1)→[0,∞), and f:[0,∞)→[0,∞) is continuous. We...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/951947 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem u′′′(t)+λg(t)f(u(t))=0, 0<t<1, u(0)=αu(η), u′(0)=u′′(1)=0, where 0<η<1, 0<α<1, λ is a positive parameter, g:(0,1)→[0,∞), and f:[0,∞)→[0,∞) is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained. |
|---|---|
| ISSN: | 2314-4629 2314-4785 |