This note is concerned with the existence of continuously differentiable solutions for the nonlinear system of differential equationsf(x'(t)) = g(t, x(t)),x(0) = x(0),where Omega is an open set containing (0, x(0)), g : Omega subset of R x R-n -> R-n is continuous and f : R-n -> R-n satisfies Im(g) subset of Im(f). The set of points x such that f is not locally Lipschitz in an open neighborhood of x is denoted by Lambda(f). We prove the existence of at least one C-1 solution x : [0, T] -> R-n to the system if f is continuous, coercive and if each y in the setf(Lambda(f)boolean OR {x is not an element of Lambda(f) : partial derivative f(x) is not of maximal rank})has exactly one preimage in R-n. (C) 2009 Elsevier Inc. All rights reserved.
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机译：该注释涉及微分方程非线性系统f（x'（t））= g（t，x（t）），x（0）= x（0）的连续可微解的存在，其中Omega是包含（0，x（0）），g的开放集：R x Rn-> Rn的Omega子集是连续的，f：Rn-> Rn满足Im（f）的Im（g）子集。 Lambda（f）表示使x在x的开放邻域中局部不是Lipschitz的点x的集合。如果f是连续的，强制的，并且setf（Lambda（f）boolean OR {x不是一个Lambda（f）的元素：偏导数f（x）的秩不是最大}）在Rn中恰好有一个原像。 （C）2009 Elsevier Inc.保留所有权利。
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