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The classical Sturm comparison and separation theorems have been generalized by M. Picone and by G. Cimmino to partial differential equations and to systems of ordinary and partial differential equations [1]. In [2] G. Cimmino has proved the Sturm theorems for mappings valued in $l^2$. Recently several authors [3, 4, 5, 6, 7] have studied the Sturm theorems for ordinary and partial equations with solutions taking their values in $𝐑$ or ${𝐑}^n$. C. Pontini [8] has proved a Sturm theorem for ordinary equations...