Foreword to the Classics Edition Preface to the First Edition Preface to the Second Edition Errata I: Preliminaries II: Existence III: Differential In qualities and Uniqueness IV: Linear Differential… Expand

where, for a fixed x, F[u] (x) is a non-linear functional of u. The results to be obtained can be considered as generalizations of some theorems of Gilbarg [5] and Stampacchia [14] in the case F [ u… Expand

The object of this note is to answer this question in the affirmative when F(x) is of class C2. (It can be mentioned that, even if F(x) is analytic, there need not exist such a map R of class C' with… Expand

where x and z are vectors (not necessarily of the same dimension). 1. Below, if x, f are vectors, I x| denotes the Euclidean length of x and x *f the scalar product of x and f. In ??1-5, there will… Expand

(1.1) M' is complete and its sectional curvatures are non-positive. In terms of local coordinates x = (x, . . . , x) on M and y = (y, . . . , y) on M', let the respective Riemann elements of… Expand

For the equationy" + q(t)y = 0, we derive necessary conditions for nonoscillation in terms of "general means" of Q (t) f q ds. 1. Main theorem. The object of this note is to obtain necessary… Expand

occurs in a number of places; cf., e.g., [5, pp. 226-227], where a>=oo, q(t)^0, and the question of the existence of a solution r(t) >0 of (1.4) for large / is discussed in connection with the study… Expand