The aim of this paper is to survey some researches of the author on the invertibility in the large of smooth functions. We focus on the finite dimension (even if the results have analogues in Banach spaces). We show a criterion for the invertibility on compact domains of C^1 mappings which is obtained by means of ideas in Lyapunov Stability. We also show a sufficient condition for the invertibility on the whole R^n, via auxiliary proper functions, and a simple consequence of it. Moreover we use auxiliary proper functions to give a necessary and sufficient condition for the bijectivity of mappings R^n to R^n from which the classical Theorems of Hadamard and Caccioppoli are easily obtained (for local diffeomorphisms R^n to R^n).
On the inversion of smooth functions
ZAMPIERI, Gaetano
1993-01-01
Abstract
The aim of this paper is to survey some researches of the author on the invertibility in the large of smooth functions. We focus on the finite dimension (even if the results have analogues in Banach spaces). We show a criterion for the invertibility on compact domains of C^1 mappings which is obtained by means of ideas in Lyapunov Stability. We also show a sufficient condition for the invertibility on the whole R^n, via auxiliary proper functions, and a simple consequence of it. Moreover we use auxiliary proper functions to give a necessary and sufficient condition for the bijectivity of mappings R^n to R^n from which the classical Theorems of Hadamard and Caccioppoli are easily obtained (for local diffeomorphisms R^n to R^n).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.