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Weak solutions of given problems are sometimes not necessarily unique. Relevant solutions are then picked out of the set of weak solutions by so-called entropy conditions. Connections between the original and the numerical entropy condition were often discussed in the particular case of scalar conservation laws, and also a general theory was presented in the literature for general scalar problems. The entropy conditions were realized by certain inequalities not generalizable to systems of equations...

In questa Nota è generalizzato un teorema di R. Reissig sull'esistenza di una soluzione periodica dell'equazione differenziale non autonoma $$x^{(n+1)}+a_1{x}^{(n)}+\mathrm{\cdots }+a_n{x}^{\prime }+f(t,x)=e(t)$$.