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

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  • Global Weak Convergence of Successive A

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説明

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, ∞].

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