Donato Fortunato

Bio: Donato Fortunato is an academic researcher from University of Bari. The author has contributed to research in topics: Nonlinear system & Maxwell's equations. The author has an hindex of 28, co-authored 104 publications receiving 4221 citations. Previous affiliations of Donato Fortunato include Instituto Politécnico Nacional & University of Sussex.

Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity

Abstract: CRITICAL POINT THEOREMS AND APPLICATIONS TO SOME NONLINEAR PROBLEMS WITH -STRONG” RESONANCE AT INFINITY + P. BARTOLO and V. BENCI Istituto di Matematica Applicata. Via Re David. X0-Bari. Ital) and Istituto di Analisi Matematica. Palazzo Ateneo. L’ia Scolai. 2-Bari. Italy (Received in revised form 20 December 1952)

An eigenvalue problem for the Schrödinger-Maxwell equations

Abstract: In this paper we study the eigenvalue problem for the Schrödinger operator coupled with the electromagnetic field E,H. The case in which the electromagnetic field is given has been mainly considered ([1]–[3]). Here we do not assume that the electromagnetic field is assigned, then we have to study a system of equations whose unknowns are the wave function ψ = ψ(x, t) and the gauge potentials A = A(x, t), φ = φ(x, t) related to E,H. We want to investigate the case in which A and φ do not depend on the time t and ψ(x, t) = u(x)e, u real function and ω a real number In this situation we can assume A = 0 and we are reduced to study the existence of real numbers ω and real functions u, φ satisfying the system

Solitary waves of the nonlinear klein-gordon equation coupled with the maxwell equations

Abstract: This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

Recent Developments in General Relativity

Abstract: General Perspectives.- Special Relativity at Action in the Universe.- String Theory and General Relativity.- Virgo - a Laser Interferometer for Gravitational Wave Detection.- A Space Test of General Relativity.- Canonical "Loop" Quantum Gravity and Spin Foam Models.- A Possible Way to Define an Effective Cosmological Constant in Scalar-Tensor Cosmologies.- A Microscopic Approach to Nuclear Physics: from Deuteron to Neutron Stars.- Perspectives in the Research of GravitationalWaves: Omnidirectional Resonant Detectors.- The Entropy of Black Holes via Noether's Theorem.- Dual Lagrangian Theories.- The Boundary State Description of D-Branes.- The N-body Problem in Tetrad Gravity: A First Step towards a Unified Description of the Four Interactions.- Applications of Calculus of Variations to General Relativity.- The Search for Gravitational Waves with Resonant Detectors.- Cauchy-Perturbative Matching and Outer Boundary Conditions.- Branes in Anti-de Sitter Space-Time.- Black Hole Entropy.- Gravitational Wave Astronomy from Space.- Bar Mode Instability in Relativistic Rotating Stars.- Recent Results.- General Relativity and Theory of Gravitation.- Theoretical Relativity: Classical Topics.- Why is the Gravitational Mass Equal to the Inertial Mass?.- Multiplicity of Timelike Geodesics in Splitting Lorentzian Manifolds.- Gravitational Collapse of Fluid Bodies and Cosmic Censorship: Analytic Insights.- Black Holes and Solitons.- The Prolongation Problem for the Heavenly Equation.- Time Extremizing Trajectories of Massive and Massless Objects in General Relativity.- Null Geodesics Joining Two Submanifolds in Stationary Lorentzian Manifolds.- Analytic Solution of Regge-Wheeler Differential Equation for Black Hole Perturbations in Radial Coordinate and Time Domains.- Quantum Gravity.- Problems in Quantum General Relativity and Gravitation.- Problems in Quantum General Relativity and Gravitation.- Foundational Problems in Quantum Gravity.- Foundational Problems in Quantum Gravity.- Foundational Problems in Quantum Gravity.- Foundational Problems in Quantum Gravity.- A Review of Recent Results of the ? -Function Regularization Procedure in Curved Spacetime.- Solitons in Three Space Dimensions as a Model for Relativistic Particles.- Relativistic Astrophysics and Cosmology.- Relativistic Astrophysics and Cosmology.- Voids in Open Universes.- Non-Stationary Accretion onto Black Holes.- Stochastic Backgrounds of Gravitational Waves from Compact Sources.- Experimental Gravitation.- Sights of Experimental Gravity.- Mechanical Isolation of Gravitational Wave Antennae: Present and Future.- Off-Line Subtraction of Seismic Newtonian Noise.- de Broglie-like Oscillation s of Spacetime.- Testing Newton's Inverse Square Law.

An existence result for nonlinear elliptic problems involving critical Sobolev exponent

Abstract: In this paper we consider the following problem: (1) { − Δ u − λ u = | u | 2 ⁎ − 2 ⋅ u u = 0 on ∂ Ω 2 ⁎ = 2 n / ( n − 2 ) where Ω ⊂ Rn is a bounded domain and λ ∈ R. We prove the existence of a nontrivial solution of (1) for any λ > 0, if n ⩾ 4.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Entanglement detection

Abstract: How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given on the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.

Bell's theorem. Experimental tests and implications

Abstract: Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics. The theorem shows that essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a single experimental arrangement. Moreover, the predictions by those theories must significantly differ from those by quantum mechanics. Experimental results evidently refute the theorem's predictions for these theories and favour those of quantum mechanics. The conclusions are philosophically startling: either one must totally abandon the realistic philosophy of most working scientists, or dramatically revise out concept of space-time.

Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States

Abstract: Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.

On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN

Abstract: Using the ‘monotonicity trick’ introduced by Struwe, we derive a generic theorem. It says that for a wide class of functionals, having a mountain-pass (MP) geometry, almost every functional in this class has a bounded Palais-Smale sequence at the MP level. Then we show how the generic theorem can be used to obtain, for a given functional, a special Palais–Smale sequence possessing extra properties that help to ensure its convergence. Subsequently, these abstract results are applied to prove the existence of a positive solution for a problem of the formWe assume that the functional associated to (P) has an MP geometry. Our results cover the case where the nonlinearity f satisfies (i) f(x, s)s−1 → a ∈)0, ∞) as s →+∞; and (ii) f(x, s)s–1 is non decreasing as a function of s ≥ 0, a.e. x → ℝN.