- Research Article
- Open Access
Positive Solutions of a Nonlinear Three-Point Integral Boundary Value Problem
© J. Tariboon and T. Sitthiwirattham. 2010
- Received: 4 August 2010
- Accepted: 18 September 2010
- Published: 20 September 2010
- Banach Space
- Partial Differential Equation
- Unique Solution
- Ordinary Differential Equation
- Functional Equation
and so forth.
Then and correspond to the superlinear case, and and correspond to the sublinear case. By the positive solution of (1.2)-(1.3) we mean that a function is positive on and satisfies the problem (1.2)-(1.3).
Throughout this paper, we suppose the following conditions hold:
The proof of the main theorem is based upon an application of the following Krasnoselskii's fixed point theorem in a cone.
Theorem 1.1 (see ).
be a completely continuous operator such that
We now state and prove several lemmas before stating our main results.
This completes the proof.
Now we are in the position to establish the main result.
The authors would like to thank the referee for their comments and suggestions on the paper. Especially, the authors would like to thank Dr. Elvin James Moore for valuable advice. This research is supported by the Centre of Excellence in Mathematics, Thailand.
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