Yuji Liu
Abstract:
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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