A constructive proof of the Cauchy–Kovalevskaya theorem for ordinary differential equations

Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations

In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.

A Subspace Theorem for Ordinary Linear Differential Equations

The study of the S-unit equation for algebraic numbers rests very heavily on Schmidt's Subspace Theorem. Here we prove an effective subspace theorem for the differential funrtion field case, which should be valuable in the proof of results concerning the S-unit equation for funrtion fields. Theorem 1 states that either O r d ^ L . V L J has a given upper bound where ^(PJ . I^P) , . . . , ! , , ...

Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces

We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

Uniqueness Theorem for Ordinary Differential Equations with Hölder Continuity

A Constructive Proof of Gleason's Theorem