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On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations

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Abstract

In the present paper we give some necessary conditions that satisfy the solutions of an infinite system of ordinary differential equations. We investigate the behavior of the solutions of a general system of equations, regarding the norm of a Banach function space based on a vector measure. To this aim we construct a vector measure by an standard procedure. Assuming that the solution of each individual equation of the system belongs to a Banach function space based on scalar measures we deduce, with natural conditions, that a solution of such system belongs to a Banach function space based on a vector measure. We also give an example of a system of non-linear Bernoulli equations and show the relation with an equation involving the integral operator.

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  1. Departamento de Educación, Universidad Internacional de la Rioja, Paseo de la Castellana, 163, 28046, Madrid, Spain

    Orlando Galdames Bravo

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  1. Orlando Galdames Bravo
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Correspondence to Orlando Galdames Bravo.

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Galdames Bravo, O. On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations. Mediterr. J. Math. 12, 939–956 (2015). https://doi.org/10.1007/s00009-014-0445-7

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  • DOI: https://doi.org/10.1007/s00009-014-0445-7

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