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