Nonoscillation theorems for a class of nonlinear differential equations

Abstract

of which (1) is the Euler equation, proves to be utterly unsuitable for our purposes. The main reason for this is the fact that the family of extremals of this problem which pass through a point do not form a field and that, therefore, the classical stfficient criteria for the existence of extrema become unapplicable. \Ve shall show that the proper problem is that of mininmizing the generalized Rayleigh quotient