Addolorata Salvatore

Multiplicity results of an elliptic equation with non-homogeneous boundary conditions

where Ω is an open smooth bounded subset of R , N ≥ 2, g : ∂Ω→ R is a given continuous function and p > 2 is fixed. If g ≡ 0, it is well known that (1.1) has infinitely many distinct solutions for 2 2 if N = 2. Such results have been proved by using variational methods also for more general odd nonlinearities at the beginning of 70’s (see e.g. [2], [3], [6], [9], [11] and references therein). In all these papers a fundamental role is played by the fact that the energy functional is even in a Banach space, hence it is possible to use a modified version of the classical Ljusternik–Schnirelman theory and the properties of the genus for symmetric sets. On the contrary, if g 6≡ 0 the more general boundary value problem (1.1) loses its symmetry and the previous recalled arguments do not hold. In fact, it is well

Radial solutions of semilinear elliptic equations with broken symmetry

The aim of this paper is to prove the existence of infinitely many radial solutions of a superlinear elliptic problem with rotational symmetry and non-homogeneous boundary data.

Multiple Solutions for Perturbed Elliptic Equations in Unbounded Domains

Abstract We look for solutions of a nonlinear perturbed Schrödinger equation with nonhomogeneous Dirichlet boundary conditions. By using a perturbation method introduced by Bolle, we prove the existence of multiple solutions in spite of the lack of the symmetry of the problem.

Light rays joining two submanifolds in space-times

Abstract Let M = Mo × R be a stationary Lorentz metric and P0, P1 be two closed submanifolds of M0. By using the Ljusternik-Schnirelman theory and variational tools, we prove the influence of the topology of P0 and P1 on the number of lightlike geodesics in P0 joining P0 × {0} to P1 × R.

Existence and multiplicity of normal geodesics in Lorentzian manifolds

In this paper we shall prove some results pertaining to the existence and multiplicity of normal geodesics joining two given submanifolds of an orthogonal splitting Lorentzian manifold. To this aim, we look for critical points of an unbounded suitable functional by using a Saddle-Point Theorem and the relative category theory.

Multiple solutions for semilinear elliptic systems with non-homogeneous boundary conditions

Since the early seventies, many authors have widely investigated existence and multiplicity of solutions for semilinear elliptic problems with Dirichlet boundary conditions, especially by means of variational methods (see [22] and references therein). In particular, if ’ is a real L2-function on a bounded domain ⊂ Rn, p? 2 and pi 2∗ if n? 3 (here, 2∗ = 2n n−2 ), the following model problem   −6u= |u|p−2u+ ’ in ;

Normal geodesics in stationary Lorentzian manifolds with unbounded coefficients

Abstract Let M be a stationary manifold equipped with a Lorentz metric whose coefficients are unbounded. By using variational methods and topological tools, some existence and multiplicity results of normal geodesics joining two fixed submanifolds can be proved.

Periodic Solutions of Hamiltonian Systems: The Case of the Singular Potential

Let us consider the Hamiltonian system of 2n ordinary differential equations

Periodic solutions of dynamical systems

\left\{ {\begin{array}{*{20}{c}} {\dot p\, = \, - {H_q}\,(p,q)} \\ {\dot q\, = \,{H_p}(p,q)} \end{array}} \right.