非线性系统展开的存在域

Existence Domain of Expansions for Nonlinear Systems

研究了在实的Ｂａｎａｃｈ空间上，由算子方程描述的一类非线性系统的展开问题，还给出了求其广义幂级数展开一个存在域的直接方法．同时指出，在适当的条件下，这种广义幂级数就是我们熟知的Ｖｏｌｔｅｒｒａ级数．

The problems of expansions for nonlinear systems described by operation equations in real Banach spaces are studied and a direct method is given for obtaining an existence domain of generalized power-series expansions for these systems.In particular.it is pointed out that.under proper condi nons.this kind of generalized power-series is just well-known Volterra series.