Some P-properties for nonlinear transformations on Euclidean Jordan algebras

In this article, we introduce the concepts of P and P0 properties for a nonlinear transformation defined on a Euclidean Jordan algebra and study existence of solution in the associated complementarity problems. In particular, we show, in this general setting, that if a transformation has the P0 and R0 properties, then all associated complementarity problems have solutions. We also describe a necessary condition for a transformation to have the (global) uniqueness of solution property.