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J. Rojo
Soluciones analíticas vectoriales y numéricas de sistemas diferenciales
Pub. de la Sección de Mat. Univ. de Valladolid, 4 (1981), pp. 45-60

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Abstract:
We consider systems of linear equations
     w^1 ' = a_1^1 w^1 + ... + a_n^1 w^n + b^1
     ....................................................................
     w^n ' = a_1^n w^1 + ... + a_n^n w^n + b^n
whose coefficients a_i^j are complex-valued analytic functions, while the independent terms b^1 ... b^n are analytic functions taking values on a locally convex space E.
    We prove existence and uniqueness of analytic vector-valued solutions. In the homogeneous case, we establish the relations between the spaces of vectorial and scalar solutions.
AMS(MOS) subject classification: 46A03, 34G99

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