Global Properties of Proper Lipschitzian Maps
Bruce Pourciau · SIAM Journal on Mathematical Analysis · 1983
Equations of the form $f(x) = y$, where f is a locally Lipschitz continuous map from $R^n $ into $R^n $, arise naturally in the study of nonlinear electrical networks and integrability questions in mathematical economics. In such contexts, properties of the image $f(R^n )$ become important. In this paper we use a generalized set-valued derivative and a special degree function to study the ontoness and interiority of locally Lipschitz continuous maps.