Geodesics on nonstatic Lorentz manifolds of Reissner-Nordstrom type (Erratum).
Geodesics on non static Lorentz manifolds of Reissner-Norström type.
The brachistochrone problem with frictional forces
Geodesics on Lorentzian manifolds with quasi-convex boundary.
Dynamical systems with newtonian type potentials
On a variational theory of light rays on Lorentzian manifolds
In this Note, by using a generalization of the classical Fermat principle, we prove the existence and multiplicity of lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds, satisfying a suitable compactness assumption, which is weaker than the globally hyperbolicity.
The brachistochrone problem with frictional forces
In this paper we show the existence of the solution for the classical brachistochrone problem under the action of a conservative field in presence of frictional forces. Assuming that the frictional forces and the potential grow at most linearly, we prove the existence of a minimizer on the travel time between any two given points, whenever the initial velocity is great enough. We also prove the uniqueness of the minimizer whenever the given points are sufficiently close.
Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
Some results on the existence of geodesics in static Lorentz manifolds with singular boundary
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.
On the multiplicity of brake orbits and homoclinics in Riemannian manifolds
Let be a complete Riemannian manifold, an open subset whose closure is diffeomorphic to an annulus. If is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in starting orthogonally to one connected component of and arriving orthogonally onto the other one. The results given in [5] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating...
Dynamical systems with Newtonian type potentials
We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.
Dynamical systems with Newtonian type potentials
We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.
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