Vol. 19, No. 3, 1966

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ISSN: 0030-8730
On Liapunov functions with a single critical point

Walter Leighton

Vol. 19 (1966), No. 3, 467–472
Abstract

In this paper we discuss the geometry of the level surfaces of functions f(x) = f(x1,x2,,xn) of class C′′ in En that possess an isolated relative minimum point at the origin, and no other critical points, finite or infinite. Our principal result is that such a function satisfies the condition f(x) > f(0) for all (x)(0). The levels sets f(x) = c and the domains they bound are discussed. The results are useful in Liapunov stability theory.

Mathematical Subject Classification
Primary: 49.00
Milestones
Received: 11 March 1965
Published: 1 December 1966
Authors
Walter Leighton