The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

— Vengono riconsiderati il problema di derivata obliqua regolare e quello misto di Dirichlet-derivata obliqua regolare per le funzioni armoniche in un dominio di ${\mathbb{R}}^3$ e le questioni di completezza hilbertiana connesse già studiate in un precedente lavoro e viene data una nuova dimostrazione di un teorema di unicità.

— Si presentano alcuni risultati di esistenza e molteplicità di soluzioni positive per l'equazione $\mathrm{\Delta }u+u^{2^{*}-1}=0$ in $H_0^{\left(1,2\right)}\left(\mathrm{\Omega }\right)$, dove $\mathrm{\Omega }$ è un aperto limitato di ${\mathbb{R}}^n$ con $n\ge 3$ e $2^{*}=2n/\left(n\mathrm{—}2\right)$. Si mostra che opportune perturbazioni di $\mathrm{\Omega }$ comportano l'esistenza di soluzioni positive, che convergono a zero quando la capacità delle perturbazioni tende a zero. In particolare, si ottengono risultati di esistenza e molteplicità di soluzioni positive in alcuni aperti limitati e contrattili, non necessariamente simmetrici.

A periodic BVP for a semilinear elliptic-parabolic equation in an unbounded domain $\mathrm{\Omega }$ contained in a half-space of ${ℝ}^n$ is considered, with Dirichlet boundary conditions on the finite part of $\partial \mathrm{\Omega }$. A theorem of uniqueness of periodic solutions is proved by showing that a suitable function of the "energy" $E(x)$ is subharmonic in $\mathrm{\Omega }$ and satisfies a Phragmèn-Lindelöf growth condition at infinity.

We study general continuity properties for an increasing family of Banach spaces $S_w^p$ of classes for pseudo-differential symbols, where $S_w^{\infty }=S_w$ was introduced by J. Sjöstrand in 1993. We prove that the operators in $\mathrm{Op}\left(S_w^p\right)$ are Schatten-von Neumann operators of order $p$ on $L^2$. We prove also that $\mathrm{Op}\left(S_w^p\right)\mathrm{Op}\left(S_w^r\right)\subset \mathrm{Op}\left(S_w^r\right)$ and $S_w^p·S_w^q\subset S_w^r$, provided $1/p+1/q=1/r$. If instead $1/p+1/q=1+1/r$, then $S_w^{p}w*S_w^q\subset S_w^r$. By modifying the definition of the $S_w^p$-spaces, one also obtains symbol classes related to the $S(m,g)$ spaces.

We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...