Existence of Real Solutions of Nonlinear Equations without A Priori Normality Assumptions

被引：0

作者：

Arutyunov, A. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Trapeznikov Inst Control Sci, Moscow 117997, Russia

来源：

MATHEMATICAL NOTES | 2021年 / 109卷 / 1-2期

基金：

俄罗斯科学基金会;

关键词：

abnormal point; nonlinear equation; real solution; truncation; directional regularity; IMPLICIT-FUNCTION THEOREM; NEIGHBORHOOD;

D O I：

10.1134/S0001434621010016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The existence of real solutions of a nonlinear equation in a neighborhood of an abnormal (degenerate) point is studied. We prove that if the mapping describing this equation admits a lambda-truncation that is regular in some direction, then there exist solutions for all right-hand sides in some neighborhood of the image of the abnormal point. Under the same assumption, we prove that there exist nontrivial smooth curves passing through the abnormal point and lying on the level set of the map in question.

引用

页码：3 / 14

页数：12

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