The purpose of this U.S.-Poland cooperative project between Dr. Gary H. Meisters of the University of Nebraska and Dr. Czeslaw Olech of the Mathematics Institute of the Polish Academy of Sciences is to study globally one-to-one maps (global inverse function theorems) and their relations to nonlinear differential equations. This basic research collaboration continues a productive professional interaction between the researchers and ensures direct and continued access to the excellent work in this area being done by Polish mathematicians. The project fulfills the NSF U.S.-Eastern Europe Cooperative Science Program's objective of advancing scientific knowledge by enabling leading experts in the United States and Eastern Europe to combine complementary talents and pool resources in areas of strong mutual interest and competence.