Electron. J. Diff. Eqns., Vol. 2008(2008), No. 20, pp. 1-43.

Non-homogeneous boundary-value problems of higher order differential equations with p-Laplacian

Yuji Liu

We establish sufficient conditions for the existence of positive solutions to five multi-point boundary value problems. These problems have a common equation (in different function domains) and different boundary conditions. It is interesting note that the methods for solving all these problems and most of the reference are based on the Mawhin's coincidence degree theory. First, we present a survey of multi-point boundary-value problems and the motivation of this paper. Then we present the main results which generalize and improve results in the references. We conclude this article with examples of problems that can not solved by methods known so far.

Submitted September 27, 2007. Published February 21, 2008.
Math Subject Classifications: 34B10, 34B15, 35B10
Key Words: One-dimension p-Laplacian differential equation; positive solution; multi-point boundary-value problem; non-homogeneous boundary conditions; Mawhin's coincidence degree theory.

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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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