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Su un problema di filtrazione in un mezzo poroso non omogeneo

Vieri Benci — 1973

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

We prove the existence of a unique solution for a free boundary problem relative to the stationary flow between two water reservoirs of different levels separated by a dam of a nomhomogeneous porous medium.

A "Birkhoff-Lewis" type result for a class of Hamiltonian systems.

Vieri Benci; Donato Fortunato — 1987

Manuscripta mathematica

A Morse index for geodesics in static Lorentz manifolds.

Vieri Benci; Antonio Masiello — 1992

Mathematische Annalen

Rotation numbers for Lagrangian systems and Morse theory

Vieri Benci; Alberto Abbondandolo — 1996

Banach Center Publications

Existence of geodesics for the Lorentz metric of a stationary gravitational field

Vieri Benci; Donato Fortunato — 1990

Annales de l'I.H.P. Analyse non linéaire

Alcune osservazioni sulla matematica non archimedea

Vieri Benci; Paolo Freguglia — 2016

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana

Questo articolo è una breve introduzione alla matematica non-archimedea. Nella prima parte passiamo in rassegna alcuni aspetti storici relativi alla critica dell'assioma di Archimede. Nella seconda parte ci proponiamo di mostrare la maggiore adeguatezza del punto di vista non archimedeo nell'analizzare la nozione di continuo euclideo.

Critical Point Theorems for Indefinite Functionals.

Vieri Benci; Paul H. Rabinowitz — 1979

Inventiones mathematicae

Three Dimensional Vortices in the Nonlinear Wave Equation

Marino Badiale; Vieri Benci; Sergio Rolando — 2009

Bollettino dell'Unione Matematica Italiana

We prove the existence of rotating solitary waves (vortices) for the nonlinear Klein-Gordon equation with nonnegative potential, by finding nonnegative cylindrical solutions to the standing equation $-\Delta u+\frac{\mu}{|y|^{2}}u+\lambda u=g(u),\quad u\in H^{1}(\mathbb{R}^{N})% ,\quad\int_{\mathbb{R}^{N}}\frac{u^{2}}{|y|^{2}}\,dx<\infty,$ where $x=(y,z)\in\mathbb{R}^{k}\times\mathbb{R}^{N-k}$ , $N>k\geq 2$ , $\mu>0$ and $\lambda\geq 0$ . The nonnegativity of the potential makes the equation suitable for physical models and guarantees the wellposedness of the corresponding Cauchy problem, but it prevents the use of standard arguments in providing the functional associated to $({\dagger})$ with bounded Palais-Smale sequences....

Some results on the existence of geodesics in static Lorentz manifolds with singular boundary

Vieri Benci; Donato Fortunato; Fabio Giannoni — 1991

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we deal with the problem of the existence of geodesies joining two given points of certain non-complete Lorentz manifolds, of which the Schwarzschild spacetime is the simplest physical example.

A nonlinear elliptic equation with singular potential and applications to nonlinear field equations

Marino Badiale; Vieri Benci; Sergio Rolando — 2007

Journal of the European Mathematical Society

We prove the existence of cylindrical solutions to the semilinear elliptic problem $- Δ u + \frac{u}{{| y |}^{2}} = f (u)$ , $u \in H^{1} (ℝ^{N})$ , $u \geq 0$ , where $(y, z) \in ℝ^{k} \times ℝ^{N - k}$ , $N > k \geq 2$ and $f$ has a double-power behaviour, subcritical at infinity and supercritical near the origin. This result also implies the existence of solitary waves with nonvanishing angular momentum for nonlinear Schr¨odinger and Klein–Gordon equations.

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