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Ordinary Differential Equations
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 DifferentialExpand
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On some non-linear elliptic differential-functional equations
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 [ uExpand
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A lemma in the theory of structural stability of differential equations
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' withExpand
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On boundary value problems for systems of ordinary, nonlinear, second order differential equations
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 willExpand
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On homotopic harmonic maps
(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 ofExpand
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On nonoscillatory linear differential equations of second order
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 necessaryExpand
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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 studyExpand
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