Electron. J. Diff. Eqns., Vol. 2008(2008), No. 92, pp. 1-14.

Existence of positive solutions for p-Laplacian three-point boundary-value problems on time scales

Hong-Rui Sun, Ying-Hai Wang

This article shows the existence of positive solutions for a class of p-Laplacian three-point boundary-value problem on time scales. By using several fixed point theorems in cones, we establish conditions for the existence of at least one, two or three positive solutions for the boundary-value problems. Our results are new even for the corresponding differential ( $\mathbb{T}=\mathbb{R})$ and difference equation ($\mathbb{T}=\mathbb{Z})$, and for the general time scales setting. An example is also given to illustrate our results.

Submitted January 26, 2007. Published July 2, 2008.
Math Subject Classifications: 34B15, 39A10.
Key Words: Time scales; p-Laplacian; positive solution; cone; fixed point.

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Hong-Rui Sun
School of Mathematics and Statistics, Lanzhou University
Lanzhou, Gansu 730000, China
email: hrsun@lzu.edu.cn
  Ying-Hai Wang
School of Physical Science and Technology, Lanzhou University
Lanzhou, Gansu 730000, China
email: yhwang@lzu.edu.cn

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