Copyright © 2010 Zhenhua Cao et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Firstly, we define an order for differential forms. Secondly, we also define the supersolution and subsolution of the -harmonic equation and the obstacle problems for differential forms which satisfy the -harmonic equation, and we obtain the relations between the solutions to -harmonic equation and the solution to the obstacle problem of the -harmonic equation. Finally, as an application of the obstacle problem, we prove the existence and uniqueness of the solution to the -harmonic equation on a bounded domain with a smooth boundary , where the -harmonic equation satisfies where is any given differential form which belongs to .