Teoria dei fasci e trasformazioni integrali per -moduli tra varietà di Grassmann
This paper concerns the sufficient conditions for the applicability of the Newton-Kantorovich method to nonlinear singular integro-differential equation with Hilbert Kernel.
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.