Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem
- Tiaoxia Dun
- Pengyu Chen
Publication date
January 2014
DOI Publisher
Hindawi Limited ISSN
2314-4629 Journal
2314-4785Abstract
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
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