Geometry of PDE's. II: Variational PDE's and integral bordism groups

In the framework of the geometry of PDE's, we classify variational equations of any order with respect to their formal properties. Following our previous results [A. Prastaro, Quantized Partial Differential Equations, World Scientific, Singapore, 2004], we relate constrained variational PDE's to their integral bordism groups. In this way we are able to characterize global solutions of constrained variational PDE's and to relate them to the structure of global solutions for the corresponding constraint equations. Some applications are also considered. (c) 2005 Elsevier Inc. All rights reserved.