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Si dà una condizione sufficiente ad assicurare il carattere fortemente oscillatorio dei sistemi ellittici del tipo $$\sum _{i,j=1}^n{D}_i(A_{ij}(x)D_{j}u)+C(x)u=0.$$ Con questo risultato si estendono vari criteri noti relativi al caso di una sola equazione.

MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.

Gli Autori considerano l'equazione $$y^{\prime \prime }+p(t)g(y)=f(t)$$ con $p(t)$, $f(t)$ continue in $[0,\mathrm{\infty })$, $p(t)=0$, $g(t)$ continue in $(-\mathrm{\infty },\mathrm{\infty })$ e sotto opportune condizioni per $p(t)$, $g(y)$, $f(t)$ provano che tutte le soluzioni della (1) sono oscillanti.

We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the...