Global Weak Convergence of Successive Approximations for Nonlinear Ordinary Differential Equations in Banach Spaces

摘要

The global existence of the solutions of the Cauchy problem x^′=f(t, x), x(0)=x_0∈E in a Banach space E are studied. We give a sufficient condition for the above equation to have a unique global solution, and prove that the successive approximations for the above equation converge weakly uniformly to the unique solution on any bounded interval of [0, ∞].