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Variación de las raices características de una ecuación diferencial de segundo orden con coeficientes periódicos

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Summary

The variability range of the characteristic roots of a second order differential equation y″+qy=0 is determined when q range in the family of measurable periodic functions of period ω satisfying the inequalities

$$a \leqslant q(x) \leqslant b and \sigma _1 \leqslant \int\limits_0^\omega {q(x)dx \leqslant \sigma _2 } $$

.

In the progress of this research two integers n1 and n2 appear, which are actually the smallest and the largest numbers of zeros of the solutions y≠0 of those equations in the interval [0, ω).

As a application of these results necessary and sufficient conditions, to be fulfilled by a, b, σ1 and σ2 in order to be stable the equation y″+qy=0, are given for every function belonging to that family. Finaly, these results are extended for the complete equation y″+py'+qy=0.

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La mayor parte de este trabajo ha sido realizada en Florencia con una pensión de estudios del Ministerio de Educación Nacional de España. No podemos dejar de manifestar aquí nuestro egradecimiento al Prof.G. Sansone por el estimulo y facilidades que nos ha dado para consultar la biblioteca del Instituto “Ulisse Dini”.

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R.-Salinas, B. Variación de las raices características de una ecuación diferencial de segundo orden con coeficientes periódicos. Annali di Matematica 52, 107–161 (1960). https://doi.org/10.1007/BF02415673

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