Вычислительная математика - ИСЭМ СО РАН
Вычислительная математика - ИСЭМ СО РАН
Вычислительная математика - ИСЭМ СО РАН
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IMPLICIT FUNCTION THEOREM IN SECTORIAL QUASI-<br />
NEIGHBORHOODS<br />
N.A. Sidorov, R.Y. Leontyev<br />
Institute of Mathematics, Economics and Computer Science of Irkutsk State University, Irkutsk<br />
e-mail: sidorov@math.isu.runnet.ru, lev_roma@bk.ru<br />
Abstract. We consider nonlinear operational equation F (x, λ) = 0 with condition F (0, 0) ≡ 0.<br />
Operator F x (0, 0) is not continuously inversible. We costruct continuous solutions x(λ) → 0 as λ → 0<br />
in open set S of linear normalized space Λ. Zero belongs to frontier of set S. Solution existence<br />
theorems we have illustrated by examples.<br />
Key words: banach space, implicit function theorem, sectorial quasi-neighborhoods, nonlinear<br />
operator equation, linear normalized space, two-point boundary problem<br />
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