Electron. J. Diff. Eqns., Vol. 2008(2008), No. 96, pp. 1-52.

Solutions to second order non-homogeneous multi-point BVPs using a fixed-point theorem

Yuji Liu

In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs) of second order differential equations with the one-dimensional p-Laplacian. These problems have a common equation (in different function domains) and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several known ones and are illustrated by examples. It is also shown that the approach for getting three positive solutions by using multi-fixed-point theorems can be extended to nonhomogeneous BVPs. The emphasis is on the nonhomogeneous boundary conditions and the nonlinear term involving first order derivative of the unknown. Some open problems are also proposed.

Submitted March 3, 2008. Published July 25, 2008.
Math Subject Classifications: 34B10, 34B15, 35B10.
Key Words: Second order; p-Laplacian; positive solution; mixed type multi-point boundary-value problem.

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Yuji Liu
Department of Mathematics
Guangdong University of Business Studies
Guangzhou 510320, China
email: liuyuji888@sohu.com

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