Abstract
In the article, new sufficient conditions of the extremum of the multivariable functions are shown. New sufficient tests of the stability and the asymptotic stability of gradient systems are stated.
Highlights
New sufficient conditions of the extremum of the multivariable functions are shown.
Что если функция f дифференцируема в точке x0 = 0, то условие ∇f(0) = 0 является необходимым условием экстремума.
Пусть f – непрерывно дифференцируема в проколотом шаре BH и для каждого 0 < r < H и любого x ∈ MSr верно неравенство
Summary
New sufficient conditions of the extremum of the multivariable functions are shown. Что если функция f дифференцируема в точке x0 = 0, то условие ∇f(0) = 0 является необходимым условием экстремума. Пусть f – непрерывно дифференцируема в проколотом шаре BH и для каждого 0 < r < H и любого x ∈ MSr верно неравенство
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