Banach空间中的幂级数方程

A Power Series Equation in Banach Space

本文考虑Banach空间中形如x=u+sum from k=1 to ∞(a_kx^k)的幂级数方程,建立了一个比较定理,并将其应用于一定的非线性积分方程.

A power series equation in Banach space of the form x=u+ isconsidered. By means of the principle of contraction mapping, a comparison theorem is developed which describes the relation between the equationx =u+ another power series equation x= u +. Some re-suits concerning the solutions for the first equation are obtained from certain information about the solutions for the second equation that isprobably simpler than the initial equation. The results have been appliedto the so-called Hammerstein integral equation of the form x(t) = G(t,s)f(s,x(s))ds. Specific examples are considered and certain numerical results are obtained.