论文标题
关于全局隐式函数定理的扩展
On an extension of a global implicit function theorem
论文作者
论文摘要
我们研究了Banach空间开放子集定义的方程式的全球隐式函数的存在。相对于第二个变量的部分衍生物只需要左右而不是可逆。概括已知结果，我们提供了足够的标准，可以易于检查。这些条件本质上依赖于一组零和适当的BANACH空间以及相应的生长结合之间的差异性。这些预测进一步允许考虑在与第一个变量相对应的所有开放子集上定义全局隐式函数的情况。
We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible. Generalizing known results, we provide sufficient criteria which are easy to check. These conditions essentially rely on the existence of diffeomorphisms between the respective projections of the set of zeros and appropriate Banach spaces, as well as a corresponding growth bound. The projections further allow to consider cases where the global implicit function is not defined on all of the open subset corresponding to the first variable.
