Vieri Benci

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

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

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

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.

Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology

AbstractWe use Morse theory to estimate the number of positive solutions of an elliptic problem in an open bounded setΩ ∉ ℝN. The number of solutions depends on the topology ofΩ, actually onPt(Ω), the Poincaré polynomial ofΩ. More precisely, we obtain the following Morse relations:

On the existence of multiple geodesics in static space-times

\sum\limits_{u \in K} {t^{\mu \left( u \right)} } = tP_t \left( \Omega \right) + t^2 [P_t \left( \Omega \right) - 1] + t\left( {1 + t} \right)\underset{\raise0.3em\hbox{

Numerosities of labelled sets: a new way of counting

\smash{\scriptscriptstyle\thicksim}

Solitons and the electromagnetic field

}}{O} \left( t \right)

Alpha-theory: An elementary axiomatics for nonstandard analysis

, where