This is a U.S.-China cooperative research project between Dr. Zhi-Qiang Wang, Utah State University and Professor Jia-Quan Liu, Peking University to study quasilinear elliptic partial differential equations using variational methods. The research problem is of great interest and importance to mathematics communities and can provide useful tools to physical scientists, especially those involved in the micromaterials research. Both the U.S. and the Chinese scientists are experts in this area, and the results are mutually beneficial. This research project will be jointly supported by the NSF and the National Natural Science Foundation of China.