Continuous Selections and Invertibility of Nonsmooth Maps Between Banach Spaces
研究了巴拿赫空间中具有伪雅可比矩阵的非光滑映射的局部满射性、连续选择的存在性和可逆性，给出了连续选择存在的充分条件，并推广了经典Bartle-Graves选择定理。
Abstract In the setting of Banach spaces, we address the problems of local surjectivity, existence of a continuous selection and invertibility for nonsmooth maps which admit a suitable pseudo-Jacobian. We obtain a general sufficient condition for the existence of a continuous selection. As a consequence, we recover from our result the classical Bartle-Graves selection theorem for linear maps. We also obtain a sufficient condition for local invertibility, which in particular applies to certain Gâteaux differentiable maps.