Qualitative properties of ground states for singular elliptic equations with weights

Abstract

In a series of papers the question of uniqueness of radial ground states of the equation Delta u + f(u) = 0 and of various related equations has been studied. It is remarkable that throughout this work (except in very special circumstances) nowhere is a spatially dependent term taken into consideration. Here we shall make a first attempt to study the uniqueness of ground states for such spatially dependent equations and to establish qualitative properties of solutions for this purpose.