We show that the minimization of the Lagrangian action functional on suitable classes of symmetric loops yields collisionless periodic orbits of the nbody problem, provided that some simple… (More)

In this paper we study a class of stationary states for reaction–diffusion systems of k ≥ 3 densities having disjoint supports. For a class of segregation states governed by a variational principle… (More)

We extend to the case of many competing densities the results of the paper [7]. More precisely, we are concerned with an optimal partition problem in N -dimensional domains related to the method of… (More)

In this paper we give an unified approach to some questions arising in different fields of nonlinear analysis, namely: (a) the study of the structure of the Fučík spectrum and (b) possible variants… (More)

Positivity, essential self-adjointness, and spectral properties of a class of Schrödinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficient… (More)

We consider periodic and quasi-periodic solutions of the three-body problem with homogeneous potential from the point of view of equivariant calculus of variations. First, we show that symmetry… (More)

We study the qualitative properties of a limiting elliptic system arising in phase separation for Bose-Einstein condensates with multiple states: ∆u = uv in R, ∆v = vu in R, u, v > 0 in R.… (More)

The validity of Sundman-type asymptotic estimates for collision solutions is established for a wide class of dynamical systems with singular forces, including the classical N–body problems with… (More)

We consider a semilinear elliptic equation on a smooth bounded domain Ω in R2, assuming that both the domain and the equation are invariant under reflections about one of the coordinate axes, say the… (More)